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"Reliable Computing"From the Editor (in Russian) 2 From the Editor 6 A. G. Yakovlev Interval computations - subject of research and useful tool (in Russian) 10 A. G. Yakovlev Interval computations - subject of research and useful tool 27 J. Herzberger, D. Bethke On two algorithms for bounding the inverses of an interval matrix 44 B. S. Dobronets, V. I. Senashov On interval extension of some classes of functions 54 R. B. Kearfott, Chenyi Hu, Manuel Novoa III A review of preconditioners for the interval Gauss-Seidel method 59 E. A. Musaev Narrowing of intervals by partial derivatives 86 S. P. Shary On compatibility of linear tolerance problem 92 B. V. Paluh, B. V. Vasilyov, V. L. Perov Application of interval mathematics for solving technical diagnostics tasks of non-stop manufacture in chemical industry 99
V. S. Zjuzin Review of the book: H. Bauch, K.-U. Jahn, D. Oelschlaegel, H. Suesse, V. Wiebigke "Interval Mathematics (Theory and Application)" (H. Bauch, K.-U. Jahn, D. Oelschlaegel, H. Suesse, V. Wiebigke Intervallmathematik (Teorie und Anwendungen). - Leipzig, BSB B. G. Teubner Verlagsgesellschaft, 1987, 260 S. (Mathematisch-Naturwissenschaftliche Bibliothek, Band 72)) 105 E. A. Musaev Interval Methods for Numerical Computation West Germany, Oberwolfach, 3 - 10. 3 1990 (Information on international meeting) 108 S. P. Shary 7-th All-Union Workshop in Interval Mathematics (Information) 111 Requirements for manuscript preparation (in Russian) 113 Requirements for manuscript preparation 114 Contents 115
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Interval computations. - 1991. - N 2. - 134 p.
From the Editor 2
From the Editor (in Russian) 4
MATHEMATICAL RESEARCHES
S. Shary
Optimal solution of interval linear
algebraic systems. I 7
V. Kreinovich, A. Bernat, E. Villa, Y. Mariscal
Parallel Computers. Estimate errors caused by
imprecise data 31
COMPUTER MEANS
R. Hammer, M. Neaga, D. Ratz, D. Shiryaev
PASCAL-XSC: A new language for scientific
computing 47
ADVERTISEMENT
The full translation into Russian of ANSI/IEEE
standards on computer arithmetic 82
Program package ASIAS 83
Program package ASIAS (in Russian) 84
REVIEWS AND ABSTRACTS
P. S. Pankov
Review of the new monograph:
Dobronets B. S., Shaydurov V. V. Two-sided
numerical methods 85
MEETINGS
Actual problems of applied mathematics. All-Union
conference. Saratov, May 20-22, 1991. A brief
report (A. V. Zakharov) 87
Actual problems of applied mathematics. All-Union
conference. Saratov, May 20-22, 1991. A brief
report (A. V. Zakharov, in Russian) 91
A. Davidenkoff
Advanced seminar on programming languages for
scientific/engineering computation, Leningrad,
June 3-6, 1991. A summarizing report 96
Interval subject on the SCAN-1991 symposium.
Information (J. Herzberger) 107
Resolution of 8th All-Union Workshop on interval
mathematics. Bishkek, October 1-3, 1991 108
Preliminary announcement, call for papers and
further information for a conference on numerical
analysis with automatic result verification.
Lafayette, Louisiana, February 25 - March 1, 1993 110
BIBLIOGRAPHY
Bibliography of Soviet works on interval
computations. Part 1 115
REQUIREMENTS FOR MANUSCRIPT PREPARATION 123
REQUIREMENTS FOR MANUSCRIPT PREPARATION (in Russian) 125
ADDRESSES OF EDITORIAL BOARD MEMBERS 127
CONTENTS 132
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Interval computations. - 1992. - N 1. - 121 p.
From the Editor 2
From the Editor (in Russian) 4
Mathematical researches
B. S. Dobronets
On some two-sided methods for solving systems
of ordinary differential equations 6
S. M. Rump
Inclusion of the solution for
large linear systems with M-matrix 22
Applications and studies of related disciplines
A. I. Orlov
Interval statistics 44
Computer means
E. A. Musaev
Wave computations. A technique for optimal
quasi-concurrent self-validation 53
A. G. Yakovlev
Classification approach to programming
of localizational (interval) computations 61
Computer implementation
G. D. Pankova
Programming support and algorithmic language for
validating computations on ES (IBM 360/370) series
computer 86
Reviews and abstracts
A review of the book:
A. Neumaier, Interval Methods for Systems of
Equations (G. Alefeld) 96
List of abstracts from
Referativnyi Zhurnal "Matematika" for 1991 98
Meetings
Interval Mathematics and Its Applications. Workshop 100
Bibliography
Bibliography of Soviet works on interval
computations. Part II 104
Requirements for manuscript preparation 112
Requirements for manuscript preparation (in Russian) 114
Addresses of editorial board members 116
Contents 119
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Interval Computations. - 1992. - N 2. - 125 p.
From the Editor 2
From the Editor (in Russian) 4
Mathematical researches
A. F. Filippov
Ellipsoidal estimates for a solution of a system of
differential equations 6
S. P. Shary
A new class of algorithms for optimal solution of
interval linear systems 18
P. S. Pankov
Proof of finite-dimensional inequalities by means of
interval analysis 30
V. S. Zyuzin
On metrization of interval sets I(R), I(R^n) 39
Applications and studies of related disciplines
V. Kreinivich, A. Bernat, O. Kosheleva, A. Finkelstein
Interval estimates for closure-phase and
closure-amplitude in radio astronomy 51
Computer means
A. Davidenkoff
ACRITH-XSC: A programming language
for scientific/engineering computation 72
Learning
G. G. Menshikov
The teaching experience of interval computations
at the Department of applied mathematics and control
processes of St. -Petersburg University 83
Meetings
International conference "INTERVAL-92" 86
Mathematical modelling and scientific computation.
International conference.
Sozopol, Bulgaria, September 14-17, 1993 99
Reviews and abstracts
List of abstracts from
Referativnyi Zhurnal "Matematika" for 1991 105
Bibliography
Bibliography of Soviet works on interval
computations. Part III 107
Requirements for manuscript preparation 116
Requirements for manuscript preparation (in Russian) 118
Addresses of editorial board members 120
Contents 123
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Interval Computations. - 1992. - N 3. - 126 p.
From the editor 2
From the editor (in Russian) 4
From the invited editor 6
From the invited editor (in Russian) 7
A. Akunova, T. A. Akunov and A. V. Ushakov
Construction of a comparison system
for multivariate control processes
with interval state matrix 8
A. B. Babichev, O. B. Kadyrova, T. P. Kashevarova,
A. L. Semenov UniCalc as a tool for solving problems
with inaccurate and sub-definite data 13
F. Blomquist
Interval inclusions for Dawson's integral 17
A. F. Bochkov and L. A. Yakovleva
Algorithm for experimental zero-order optimization for
plant with bounded amplitude errors 27
A. F. Bochkov and N. V. Zung
Identification of nonlinear dynamic objects
using interval experimental data 31
D. M. Claudio, M. H. Escardo, and B. R. T. Franciosi
An order-theoretical approach to interval analysis 38
A. I. Demchenko, B. V. Peltsverger, O. V. Khavronin
Syntesis of transport networks structures
under conditions of uncertain
initial information 46
B. S. Dobronets
Interval methods based on
a posteriori estimates 50
I. V. Dugarova
An algorithm of interval matrix
asymptotic stability testing 56
O. B. Ermakov
Two-sided method for solving system of ordinary
differential equations with automatic determination
of guaranteed estimates 63
T. V. Evtushenko
Optimization problems for static plants
under uncertainty conditions 70
A. F. Filippov
Ellipsoidal error estimates
for Adams method 75
N. M. Glazunov
On interval extensions of computer algebra systems 80
T. Henriksen and K. Madsen
Parallel algorithms for global optimization 88
B. Kearfott, M. Dawande, K. Du and C. Hu
INTLIB: A portable Fortran-77 elementary function
library 96
N. A. Khlebalin
Interval automatic systems - theory, computer-aided
design and applications 106
A. V. Korlyukov
A new application of interval mathematics 116
International conference on interval and
computer-algebraic methods in science and engineering
(INTERVAL'94) 122
Contents 126
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Interval Computations. - 1992. - N 4. - 133 p.
V. N. Krishchuk, N. M. Vasilega and G. L. Kozina
Interval operations and functions
library for FORTRAN 77 programming
system and its practice using 2
V. G. Krymsky
Algorithmic aims of reliability provision
for large-scale dynamic systems
with interval parameters 9
G. L. Litvinov
Error auto-correction
in rational approximation 14
S. M. Markov
On the presentation of ranges
of monotone functions
using interval arithmetic 19
G. G. Menshikov
Interval co-integration of differential
equations connected
by a substitution of the variable 32
E. A. Musaev
An approach to reliable computations
with THE minimal representation 37
A. S. Narin'yani
Ne-factors and natural pragmatics:
what do the intervals represent 42
V. M. Nesterov
Estimating a range of values
of functions using extended
interval arithmetics 48
P. S. Pankov and B. D. Bayachorova
Using interval methods in cluster analysis and
verified representation of connected sets 54
P. S. Senio and P. S. Vengersky
Solving systems of special form nonlinear
equations by means of some modifications of Runge
type interval iterative method 59
S. P. Shary
On controlled solution set
of interval algebraic systems 66
D. Shiriaev
PASCAL-XSC. A portable programming system
for scientific computations 76
S. J. Simoff
Interval approximate reasoning
for expert systems 83
N. V. Skybytsky and T. Yuping
Control of the linear dynamic plant with
intervally given parameters from the guarantee
condition of the required accuracy of the solution 88
E. M. Smagina
General problem of the asymptotic steady-output
tracking for plant with interval parameters 94
I. G. Ten
Synthesis of optimal control under interval
uncertainty in models 100
A. P. Voshchinin
Some questions of application of interval
mathematics in parameter estimation and decision
making 107
J. Wolff von Gudenberg
Programming language support for scientific
computation 116
V. S. Zyuzin
The extension of the Frechet derivative concept in
the interval-segment analysis 127
Contents 133
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Interval Computations. - 1993. - N 1.
From the Editor 2
From the Editor (in Russian) 4
Mathematical researches
Vladik Kreinovich, Anatoly V. Lakeyev and Sergey I. Noskov
Optimal solution of interval
linear systems is intractable (NP-hard) 6
R. Baker Kearfott and Xiaofa Shi
A preconditioner selection heuristic
for efficient iteration with decomposition
of arithmetic expressions for nonlinear
algebraic aystems 15
Ljiljana D. Petkovic and Miroslav Trajkovic
On some optimal inclusion
approximations by discs 34
V. A. Perepelitsa and G. L. Kozina
Interval discrete models
and multiobjectivity
complexity estimates 51
Yilmaz Akyildiz and Mohammad I. Al-Suwaiyel
No Pathologies for interval Newton's method 60
Advertisement
International conference "INTERVAL'94" 73
Reviews and abstracts
N. A. Khlebalin
Review of the Book 79
N. A. Khlebalin
Review of the Book (in Russian) 84
Meetings
Mathematical modelling and scientific computation.
International conference. Sozopol, Bulgaria,
September 14-17, 1993 99
Reviews and abstracts
List of abstracts from
Referativnyi Zhurnal "Matematika" for 1991 105
Bibliography
Bibliography of Soviet works on interval
computations. Part III 107
Requirements for manuscript preparation 116
Requirements for manuscript preparation (in Russian) 118
Addresses of editorial board members 120
Contents 123
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Interval Computations. - 1993. - N 2
(Special Issue: Proceedings of the International
Conference on Numerical Analysis with Automatic
Result Verification. Lafayette, Louisiana, USA,
Feb. 25 - March 1, 1993. - Vol. 1)
From the Editor 2
From the Editor (in Russian) 3
Foreword by Prof. R. B. Kearfott 4
Fernando L. Alvarado and Zian Wang
Direct Sparse Interval Hull Computations for
Thin Non-M-Matrices 5
A. B. Babichev, O. B. Kadyrova, T. P. Kashevarova,
A. S. Leshchenko, and A. L. Semenov
UniCalc, a Novel Approach to Solving Systems of Algebraic
Equations 29
Daniel Berleant
Automatically Verified Reasoning with Both
Intervals and Probability Density Functions 48
Ole Caprani, Brian Godthaab, and Kaj Madsen
Use of a Real-Valued Local Minimum in Parallel Interval
Global Optimization 71
Iliano Cervesato, Angelo Montanari, Alessandro Provetti
On the Non-monotonic Behaviour of Event Calculus
for Deriving Maximal Time Intervals 83
Amanda E. Connell and Robert M. Corless
An Experimental Interval Arithmetic Package in Maple 120
Jeffrey S. Ely
The VPI Software Package for Variable Precision
Interval Arithmetic 135
J. Garloff
The Bernstein Algorithm 154
Gregory D. Hager
Solving Large Systems of Nonlinear Constraints with
Application to Data Modeling 169
Meetings
Applications of Interval Computations: International
Workshop 201
Requirements for manuscript preparation 205
Requirements for manuscript preparation (in Russian) 206
Addresses of the editorial board members 207
Contents 209
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Interval Computations. - 1993. - N 3
(Special Issue: Proceedings of the International
Conference on Numerical Analysis with Automatic
Result Verification. Lafayette, Louisiana, USA,
Feb. 25 - March 1, 1993. - Vol. 2)
E. R. Hansen
Computing Zeros of Functions Using Generalized
Interval Arithmetic 3
C. Hu, R. B. Kearfott, and A. Awad
On Bounding the Range of Some Elementary Functions
in FORTRAN-77 29
R. Van Iwaarden
Automatic Differentiation Applied to Unconstrained
Nonlinear Optimization with Result Verification 41
L. Jaulin and E. Walter
Guaranteed Nonlinear Parameter Estimation via
Interval Computations 61
J. B. Keiper
Interval Arithmetic in Mathematica 76
L. J. Kohout and I. Stabile
Interval-Valued Inference in Medical Knowledge-Based
System CLINAID 88
C. Falco Korn and Ch. Ullrich
Verified Solution of Linear Systems Based on Common
Software Libraries 116
B. P. Kristinsdottir, Z. B. Zabinsky, T. Csendes,
and M. E. Tuttle
Methodologies for Tolerance Intervals 133
A. Leclerc
Parallel Interval Global Optimization and
Its Implementation in C++ 148
S. M. Markov
Some Interpolation Problems Involving Interval Data 164
M. Nakamura, R. Mines, and V. Kreinovich
Guaranteed Intervals for Kolmogorov's Theorem (and Their
Possible Relation to Neural Networks) 183
Advertisement
Journal of Symbolic Computations: Special Issue on
Validated Numerical Methods and Computer Algebra 200
Requirements for manuscript preparation 202
Requirements for manuscript preparation (in Russian) 203
Addresses of the editorial board members 204
Contents 206
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Interval Computations. - 1993. - N 4
(Special Issue: Proceedings of the International
Conference on Numerical Analysis with Automatic
Result Verification. Lafayette, Louisiana, USA,
Feb. 25 - March 1, 1993. - Vol. 3)
V. M. Nesterov
How To Use Monotonicity-Type Information To Get Better
Estimates of the Range of Real-Valued Functions 3
J. Rohn
Cheap and Tight Bounds: The Recent Result by
E. Hansen Can Be Made More Efficient 13
M. J. Schaefer
Precise Zeros of Analytic Functions Using
Interval Arithmetic 22
C. A. Schnepper and M. A. Stadtherr
Application of a Parallel Interval Newton/Generalized
Bisection Algorithm to Equation-Based Chemical Process
Flowsheeting 40
M. J. Schulte and E. E. Swartzlander, Jr.
Parallel Hardware Designs for Correctly Rounded
Elementary Functions 65
L. Simcik and P. Linz
Boundary-Based Interval Newton's Method 89
O. Sirisaengtaksin and V. Kreinovich
Neural Networks That Are Not Sensitive To The
Imprecision of Hardware Neurons 100
U. Storck
Verified Calculation of the Nodes and Weights
for Gaussian Quadrature Formulas 114
I. B. Turksen
Interval Valued Fuzzy Sets and Fuzzy Connectives 125
V. M. Veliov
Computation of Integrals of Uncertain Vector Functions 143
E. Villa, A. Bernat, and V. Kreinovich
Estimating Errors of Indirect Measurement on Realistic
Parallel Machines: Routings on 2-D and 3-D Meshes
That are Nearly Optimal 154
K. Villaverde and V. Kreinovich
A Linear-Time Algorithm That Locates Local Extrema of a
Function of One Variable From Interval Measurement Results 176
A. G. Yakovlev
Multiaspectness and Localization 195
Meetings
J. Wolff von Gudenberg
International Conference INTERVAL'94 210
Advertisement 212
Requirements for manuscript preparation 214
Requirements for manuscript preparation (in Russian) 215
Addresses of the editorial board members 216
Contents 218
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Interval Computations. - 1994. - N 1. - 116 p.
From the Editor 2
From the Editor (in Russian) 3
Mathematical Research
G. Alefeld and G. Mayer
A Computer Aided Existence and Uniqueness Proof
for an Inverse Matrix Eigenvalue Problem 4
W. J. Luther and W. Otten
Verified Inclusion for Eigenvalues of Hill's Equation 28
G. L. Kozina and V. A. Perepelitsa
Interval Spanning Trees Problem:
Solvability and Computational Complexity 42
H. Schwandt
Suboptimal Enclosures for the Interval Buneman Algorithm
for Arbitrary Block Dimension 51
O. B. Ermakov
Solving Systems of Ordinary Differential Equations Using
Adams' Interpolation Method with Guaranteed Accuracy 90
Teaching
G. G. Menshikov
On Different Definitions of Interval Extension:
Problems of Teaching 96
Amendment 99
Bibliography
Bibliography of Soviet Works on Interval Computations.
Part V 100
Requirements for manuscript preparation 110
Requirements for manuscript preparation (in Russian) 111
Addresses of the editorial board members 112
Contents 114
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Interval Computations. - 1994. - N 2. - 132 p.
From the Editor 2
From the Editor (in Russian) 4
Mathematical Research
S. P. Shary
Solving the Tolerance Problem
for Interval Linear Systems 6
N. S. Dimitrova and S. M. Markov
On Validated Newton Type Method
for Nonlinear Equations 27
V. A. Podchukayev and I. M. Svetlov
An Analytical Method of Constructing
Hurwitz Interval Polynomials 52
Applications and Studies of Related Disciplines
M. Berz and G. Hoffstaetter
Exact Bounds on the Long Term Stability
of Weakly Nonlinear Systems Applied to the
Design of Large Storage Rings 68
V. Kreinovich, T. Swenson, and A. Elentukh
Interval Approach to Testing Software 90
Meetings
1st All-Russian Conference on Countinuous Logic
and Its Applications 110
1st All-Russian Conference on Countinuous Logic
and Its Applications (in Russian) 110
Bibliography
Bibliography of Soviet Works on Interval Computations.
Part VI 116
Requirements for manuscript preparation 127
Requirements for manuscript preparation (in Russian) 128
Addresses of the editorial board members 129
Contents 131
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Interval Computations. - 1994. - N 3. - 128 p.
Parallel Algorithms for Interval Computations
Foreword by the Invited Editors of the Special Issue 2
Foreword by the Invited Editors of the Special Issue
(in Russian) 4
V. Kreinovich and A. Bernat
Parallel Algorithms for Interval Computations:
An Introduction 6
E. Lyager
Finding Local Extremal Points by Using Parallel
Interval Methods 63
K. Madsen and O. Toft
A Parallel Method for Linear Interval Equations 81
M. Plum
Enclosures for Solutions of Parameter-Dependent
Nonlinear Elliptic Boundary Value Problems:
Theory and Implementation on a Parallel Computer 106
Requirements for manuscript preparation 122
Requirements for manuscript preparation (in Russian) 123
Addresses of the editorial board members 124
Contents 126
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Interval Computations. - 1994. - N 4. - 128 p.
Proceedings of SCAN-93
Foreword by Prof. H. Stetter 2
Foreword by Prof. H. Stetter (in Russian) 3
S. Christiansen
Interval Methods and Condition Numbers
of Linear Algebraic Systems 4
M. Daumas and D. W. Matula
Rounding of Floating Point Intervals 28
M. Daumas, Ch. Mazenc, and J.-M. Muller
Towards a User Transparent Interval Arithmetic 46
M. T. Nakao
Numerical Verifications of Solutions
for Nonlinear Hyperbolic Equations 64
W. Luther and W. Otten
Computation of Standard Interval Functions
in Multiple-Precision Interval Arithmetic 78
E. D. Popova
Extended Interval Arithmetic
in IEEE Floating-Point Environment 100
Addresses of the editorial board members 130
Contents 132
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Interval Computations. - 1994. - Supplementum 1. - 54 p.
Bibliography of Works on Interval Computations
Published in Russian
B. S. Dobronets, R. B. Kearfott, L. V. Kupriyanova,
A. G. Yakovlev, and V. S. Zuizin,
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Reliable Computing. - 1995. - Vol. 1, No. 1. - 103 p.
Preface 3
Preface (in Russian) 5
Mathematical research
Formulas for the width of interval products
Helmut Ratschek and Jon G.~Rokne 9
Inner estimation of the united solution set of interval
linear algebraic system
Ludmila Kupriyanova 15
Why intervals? A simple limit theorem that is similar
to limit theorems from statistics
Vladik Kreinovich 33
A combined method for enclosing all solutions of nonlinear
systems of polynomial equations
Christine J\"ager and Dietmar Ratz 41
Parallel Algorithms for Interval Computations
An informal introduction to a high level language with
applications to interval mathematics
Daniel E. Cooke 65
A parallel interval method implementation for global
optimization using dynamic load balancing
Jerry Eriksson and Per Lindstr\"om 77
Meetings
Interval sessions at NAFIPS/IFIS/NASA'94
Vladik Kreinovich and Hung T.~Nguyen 93
Addresses of the Editorial Board Members 99
Information for Authors 101
Contents 103
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Reliable Computing. - 1995. - Vol. 1, No. 2. - 102 p.
(Special Issue: Parallel Algorithms for Interval Computations)
Preface (in Russian) 107
From the Editor 108
Parallel interval-based reasoning in medical
knowledge-based system CLINAID
Ladislav J. Kohout, Isabel Stabile,
Hasan Kalantar, Maria F. San-Andres, and John Anderson 109
Applications of interval computations to
earthquake-resistant engineering: How to compute
derivatives of interval functions fast
Vladik Kreinovich, David Nemir, and Efren Gutierrez 141
A reliable linear algebra library for transputer networks
Christian P. Ullrich and Roman Reith 173
Parallel accurate linear algebra subroutines
Juergen Wolff von Gudenberg 189
Addresses of the Editorial Board Members 201
Information for Authors 203
Contents 205
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Reliable Computing. - 1995. - Vol. 1, No. 3. - 162 p.
(Special Student Issue)
Editors' Introduction 209
Mathematical research
Application of interval Newton's method to chemical
engineering problems
Gopalan V. Balaji and J. D. Seader 215
Ockham's razor in interval identification
Bo H. Friesen and Vladik Kreinovich 225
An automatic and guaranteed determination of the number
of roots of an analytic function interior to a simple
closed curve in the complex plane
Jonathan Herlocker and Jeffrey Ely 239
A general iterative sparse linear solver and its
parallelization for interval Newton methods
Chenyi Hu, Anna Frolov, R. Baker Kearfott, and Qing Yang 251
Optimizing INTBIS on the CRAY Y-MP
Chenyi Hu, Joe Sheldon, R. Baker Kearfott, and Qing Yang 265
Study on sampling techniques with CMMs
Thomas J. McLean and David H. Xu 275
A new characterization of the set of all intervals, based
on the necessity to check consistency easily
Driss Misane and Vladik Kreinovich 285
Interpolation that leads to the narrowest intervals and its
application to expert systems and intelligent control
Hung T. Nguyen, Vladik Kreinovich, Bob Lea, and Dana Tolbert 299
A parallel complex zero finder
Mark J. Schaefer and Tilmann Bubeck 317
A software interface and hardware design for
variable-precision interval arithmetic
Michael J. Schulte and Earl E. Swartzlander, Jr. 325
A bright side of NP-hardness of interval computations:
interval heuristics applied to NP-problems
Bonnie Traylor and Vladik Kreinovich 343
Information
Special Issue 361
1994 Lotfi A. Zadeh Best Paper Award in the field of
fuzzy logic 362
Addresses of the Editorial Board Members 363
Information for Authors 365
Contents 367
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Reliable Computing. - 1995. - Vol. 1, No. 4. - 72 p.
Preface 371
Mathematical research
Matrix computation of subresultant polynomial remainder
sequences in integral domains
Alkiviadis G. Akritas, Evgenia K. Akritas, and Genadii I.
Malaschonok 375
Numerical methods using defects
Boris S. Dobronets 383
An estimate of the absolute value and width of the
solution of a linear system of equations with tridiagonal
interval matrix by the interval sweep method
A. N. Ostylovsky 393
Verification methods for inclusion disks
Ljiljana D. Petkovic and Miroslav Trajkovic 403
Design of a parallel linear algebra library for verified
computation
J. Wolff von Gudenberg 411
Computation of the stability radius of a Schur
polynomial: an orthogonal projection approach
Q.-H. Wu and M. Mansour 421
Meetings
International conference on interval methods and
computer aided proofs in science and engineering
INTERVAL'96 431
II Workshop on Interval Arithmetic 433
IMACS-GAMM International Symposium on Numerical Methods
and Error Bounds
S. Shary 434
Addresses of the Editorial Board Members 436
Information for Authors 438
Amendments 439
Contents 440
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Computations website
Reliable Computing. - 1996. - Vol. 2, No. 1. - 92 p.
Mathematical research
Algebraic approach to the interval linear static
identification, tolerance, and control problems, or
One more application of Kaucher arithmetic
Sergey P. Shary 3
Bounds of high quality for first kind Volterra
integral equations
Hans-Juergen Dobner 35
Variable-precision, interval arithmetic coprocessors
Michael J. Schulte and Earl E. Swartzlander, Jr. 47
Letters to the Editor
Maximum entropy and interval computations
(September notes on summer impressions)
Vladik Kreinovich 63
Information
Best student paper award
Vladik Kreinovich and Guenter Mayer 81
Call for Papers: Student Issues of Reliable Computing 81
Call for Papers: Special Issue of Reliable Computing on
Applications to Geosciences 82
Meetings
SCAN'95: International Symposium on Scientific Computing,
Computer Arithmetic and Validated Numerics
Andreas Frommer 84
SONIC'95: Student Mini-Symposium on Interval Computations
Vladik Kreinovich 86
Interval talks at the first El Paso Shell Oil Symposium
Vladik Kreinovich 88
Addresses of the Editorial Board members 89
Information for authors 91
Contents 92
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Reliable Computing. - 1996. - Vol. 2, No. 2. - 114 p.
Preface 95
Mechanising the theory of intervals using OBJ3
Marcilia A. Campos, Augusto C. A. Sampaio, and
Alexandre H. F. Brainer 97
Errors in vector processing and the library libavi.a
Tiaraju A. Diverio, Ursula A. Fernandes, and
Dalcidio M. Claudio 103
Chebyshev acceleration techniques for large complex
non Hermitian eigenvalue problems
Vincent Heuveline and Miloud Sadkane 111
Interval methods that are guaranteed to underestimate
(and the resulting new justification of
Kaucher arithmetic)
Vladik Kreinovich, Vyacheslav M. Nesterov, and
Nina A. Zheludeva 119
On the computational complexity of the solution of
linear systems with moduli
Anatoly V. Lakeyev 125
Software for high radix on-line arithmetic
Thomas Lynch and Michael J. Schulte 133
Self-correcting polynomial programs
Guevara Noubir and Henri J. Nussbaumer 139
Reducing division latency with reciprocal caches
Stuart F. Oberman and Michael J. Flynn 147
Interval approach challenges Monte Carlo simulation
Janne Pesonen and Eero Hyvonen 155
Interval operations involving NaNs
Evgenija D. Popova 161
Enclosing solutions of overdetermined systems of linear
interval equations
Jiri Rohn 167
Numerical solutions of Burgers' equation with a large
Reynolds number
Masaaki Sugihara and Seiji Fujino 173
Rank of convex combinations of matrices
Tomasz Szulc 181
Locating, characterizing and computing the stationary
points of a function
Michael N. Vrahatis and Evangelia C. Triantafyllou 187
Reviews
Applications of Reliable Scientific Computing 195
Information
Addresses of the Editorial Board members 204
Information for authors 206
Contents 207
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Reliable Computing. - 1996. - Vol. 2, No. 3. - 108 p.
Preface 211
Robust algorithms that locate local extrema of a
function of one variable from interval measurement
results: A remark
Christoph Eick and Karen Villaverde 213
Fast error estimates for indirect measurements:
applications to pavement engineering
Carlos Ferregut, Soheil Nazarian,
Krishnamohan Vennalaganti,
Ching-Chuan Chang, and Vladik Kreinovich 219
Newton's constant of gravitation and verified
numerical quadrature
Oliver Holzmann, Bruno Lang, and Holger Sch\"utt 229
Two adaptive Gauss-Legendre type algorithms
for the verified computation of definite integrals
Walter Kr\"amer and Stefan Wedner 241
A quadratic-time algorithm for smoothing
interval functions
Vladik Kreinovich and Karen Villaverde 255
Optimal interval enclosures for fractionally-linear
functions, and their application to intelligent control
Robert N. Lea, Vladik Kreinovich, Raul Trejo 265
If we measure a number, we get an interval.
What if we measure a function or an operator?
Joe Lorkowski and Vladik Kreinovich 287
New slope methods for sharper interval functions
and a note on Fischer's acceleration method
Jo\~ao B. Oliveira 299
Ordering events: Intervals are sufficient, more
general sets are usually not necessary
Alessandro Provetti 321
Reviews
Applications of Reliable Scientific Computing 329
Addresses of the Editorial Board members 332
Information for authors 334
Contents 335
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Reliable Computing. - 1996. - Vol. 2, No. 4. - 70 p.
Preface 339
Mathematical research
Linear interval equations: Computing enclosures with
bounded relative or absolute overestimation is NP-hard
Vladik Kreinovich and Anatoly V. Lakeyev 341
On the speed of convergence of the total step iterative
method for a class of interval linear algebraic systems
Marina A. Lyashko 351
Improving the efficiency index in enclosing a root of
an equation
Yixun Shi 357
Applications
Some examples using the interval data type in the
relational database model
John W. Starner 373
* * *
Paul Erdos, 1913-1996 383
Letters to the Editor
Double bubble minimizes: Interval computations help
in solving a long-standing geometric problem
Vladik Kreinovich 387
Information
Reliable Computing in 1997 389
Peter Fishburn receives von Neumann prize 390
Best student paper award
Vladik Kreinovich and Guenter Mayer 390
Meetings
WAI'96: II Workshop on Computer Arithmetic, Interval
and Symbolic Computations
Marcilia A. Campos 391
Interval'96: International Conference on Interval
Methods and Computer Aided Proofs in Science and
Engineering
J. Wolff von Gudenberg 392
Interval Talks at FUZZ-IEEE'96
Erich Peter Klement and Vladik Kreinovich 394
Addresses of the Editorial Board members 402
Information for authors 404
Contents 405
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Interval Computations. - 1996. - Supplement - 137 p.
Interval'96: International Conference on Interval Methods and
Computer-Aided Proofs in Science and Engineering
Sep 30 - oct 2, 1996, Wuerzburg, Germany
Extended Abstracts
Preface
Talks
A "Metric" Topology Compatible with Inclusion
Monotonicity on Interval Space
B. M. Acioly and B. R. Bedregal 7
Robust Stability Investigation Using Frequency
Domain Technique
F. Akmedjanov and S. Chelyshev 9
On the Evaluation of Functional Ranges Using a
Random Interval Arithmetic
R. Alt and J.-L. Lamotte 11
A Simplex-like Algorithm for Interval Linear Systems
O. Beaumont 13
An Information System Approach to Interval Mathematics
B. R. Bedregal and B. M. Acioly 15
Interval Deductions in Continuous Domain Logic
B. R. Bedregal and B. M. Acioly 17
A Numerically Rigorous Proof of Curve Veering for
a Plate
H. Behnke 19
A Fixpoint Approximate Semantics for Cooperating
Numerical Solvers
F. Benhamou and L. Granvilliers 20
A Library for Real Numbers using Cauchy's Embedded
Interval Sequences
D. Berthelot and M. Daumas 23
Fast Algorithms for the Evaluation of Partial
Derivates and their Application to Interval Slopes
C. Bliek 25
Variable Precision in Interval Computations
C. Bliek 27
Verified Calculation of the Approximation Error
Using Rational Approximation Functions
F. Blomquist 29
Existence Test for Asynchronous Interval Iteration
O. Caprani, K. Madsen, and O.Stauning 30
Role of Constraints in the Validated Solution of DAEs
G. F. Corliss and W. Lodwick 32
Interval Optimization Methods for Process Network
Synthesis
T. Csendes 33
Symbolic versus Floationg-point Detection of
Multivariate Pole Sets
A. Cuyt 34
Environment for the Hybrid Numeric Computation
A. Cuyt, Y. Godts, and B. Verdonk 35
Computer Assisted Proofs and Scientific Computing
H.-J. Dobner 36
Two-sided Multigrid Method for Elliptic Boundary
Value Problems
B. S. Dobronets 37
A Guaranteed Inclusion of Fixed Point of Difference
Operator on a Set of Interval Function with
Hausdorff Metric
O. B. Ermakov 39
Computer Assisted Proof of Chaos for Lorenz System.
Part II. Numerical Algorithms
Z. Galias and P. Zgliczynski 40
Bounds for the Range of a Multivariate Polynomial
over a Simplex
J. Garloff and R. Hungerbuehler 42
Robust Stability Analysis of Polynomials with
Polynomial Parameter Dependency
J. Garloff and M. Zettler 43
Direct Computation of All Singular Points of
Chemical Engineering Models Using Interval Methods
V. Gehrke and W. Marquardt 45
Interval Construction within Partially Ordered
Object Versions
G. Heidenreich, M. Minas, and J. Landauer 47
Proving the Existence of Equilibrum Positions of
Particle Systems
G. Heindl 49
Helios: A Modeling Language for Global Optimization
using Interval Analysis
P. Van Hentenryck and L. Michel 50
High Accuracy and High Performance Environment
C. A. Hoelbig, R. L. Sagula, U. A. Fernandes,
T. A. Diverio, and D. M. Claudio 51
A Computer Oriented Approach to Get Sharp Reliable
Error Bounds
W. Hofschuster and W. Kraemer 53
Hierarchical Constraint Propagation based on
Interval Arithmetic
E. Huellermeier 54
Interval Constraint Satisfaction - A New
Computational Basis for Spreadsheet Computations
E. Hyvoenen and S. De Pascale 56
Finding Global Minima of Maximum Functions by
Using Exclusion Functions without Derivatives
F. Kalovics and G. Meszaros 57
Some Issues Concerning Convergence of the Method
of Subdefinite Computations
T. P. Kashevarova and A. L. Semenov 59
A Case Study for the Use of Verifying BLAS in an
LAPACK like Verifying Driver-Routine for the
Solution of Linear Systems
T. Kersten 60
Investigations of Robustness of Modern Structures
for Controlled Devices of Cutting Machines of
Electric Drives
N. A. Khlebalin and A. V. Lazarev 61
Application of a Parallel Verified Block
LU-Algorithm to Process Simulation
W. Klein 62
Verified Modelling on Circuit Simulation
W. Klein 63
On Interval-valued Hermite Splines
V. V. Kobkov 64
On the Interval Problems on Graphs
G. L. Kozina and V. A. Perepelitsa 65
The Analysis of Complex Dynamic Systems with
Interval Models: Decomposition-Based Technique
V. Krymsky and A. Yunusov 67
Diagrammatic Representation of Interval Space in
Proving Theorems about Interval Relations
Z. Kulpa 69
Robust Observer for Linear Dynamic Objects in the
Class of Ellipsoidal Sets
N. N. Kussul 71
Each Vertex of the Set of Solutions of a Strongly
Regular Interval System of Linear Equations is
Polynomially Computable
A. V. Lakeyev 73
Matrix Games with Interval Parameters
V. I. Levin 75
Interval Computations and the Effect of Error
Auto-Correction
G. L. Litvinov 76
Idempotent Mathematics and Scientific Calculations
G. L. Litvinov, V. P. Maslov, and A. Y. Rodionov 77
Approximation Error and Error Accumulation for the
Landen Transformation
W. Luther and W. Otten 79
On the Algebra of Intervals
S. Markov 81
Interval Arithmetic in a Verification Condition
Generator
W. D. Maurer 82
On Expanding Iterations
G. G. Men'shikov 84
Set of Feasible Coefficients for Systems of
Linear Interval Equations
F. Mraz 86
Topological Methods in Computer Assisted Proofs
in Dynamics
M. Mrozek 87
A Computational Approach for the Estimates of
Constants Related to the Numerical Verification
Method for Boundary Value Problems
M. T. Nakao 88
Interval and Twin Arithmetics
V. Nesterov 89
A Relation Between Morphological and Interval
Operations
A. T. Popov and S. M. Markov 91
Distributivity of the Directed Intervals and its
Computer Algebra Applications
E. D. Popova 93
On Optimal Interval Bounds for Reachable Set of
Dynamic Systems
A. Rogalev 94
Complexity of Some Linear Problems with
Interval Data
J. Rohn 96
Concurrent Cooperating Solvers over the Reals
M. Rueher and C. Solnon 97
Intervals as Real Numbers Specification
R. Santiago and B. M. Acioly 99
Production Planning Using Uncertain Data
R. Schmieder, J. Schulze, and S. Kutscher 101
Algebraic Approach in the "Outer Problem" for
Interval Linear Equations
S. P. Shary 102
Fast and Accurate Higher-Order Derivatives of
Vector Functions Represented by Fortran 90/77
or C/C++ Codes
D. Shiriaev 104
A New Approach to the Modal Regulator Synthesis
for Interval Plants with Scalar Input
Ye. H. Smagina 105
Interval Mathematical Model and Solution Method
of The Rectangles Placement Problem
Yu. G. Stoyan and T. Ye. Romanova 107
Generalized Interval Arithmetic
J. Tupper 108
The Evaluation of Effectiveness of a Method of
Solving the Interval Systems of Algebraic Equations
and their Applications
N. M. Vasilega and G. N. Gaponenko 109
Verification of Floating-Point Arithmetic
D. Verschaeren 110
A Stopping Criterion for Rootfinding Methods
M. N. Vrahatis and D. G. Sotiropoulos 111
Intervals and other Fortran 2000 Requirements for
Scientific Computing
W. Walter 112
H-infinity-control using Polynomial Matrices and
Interval Arithmetic
J. K. Weinhofer and W. C. Haas 113
Verified Computation of the Jacobi-Functions
K. Werner 114
Computer Assisted Proof of Chaos for Lorenz System.
Part I. TS-maps.
P. Zgliczynski and Z. Galias 116
Posters
Solving Algebraic Equations on Intervals
B. M. Acioly 117
Verified Solving on Nonlinear Algebraic Systems
in Maple
N. S. Dimitrova 119
On Interval Mathematical Assistant
N. G. Glazunov 121
Interval Arithmetic and Parallelism
C. L. Hoeher, L. G. L. Fernandes, P. W. de Oliveira,
T. A. Diverio, and P. O. A. Navaux 123
Interval Analysis Algorithms for Robust
Absolute Stability
L. Kolev, D. Valtchev, and V. Borshukova 125
Design of Efficient Reusable Software Components
for Scientific Computing
M. Lerch 127
Interval Linear Programming
V. I. Levin 129
Some Aspects of Interval Geometry
Yu. G. Stoyan 130
Interval and Multiinterval Extensions in
Subdefinite Models
V. Telerman, V. Sidorov, and D. Ushakov 131
Approximation of Function by Algebraic Polynomials
Close to the Best Ones
V. S. Zyuzin 133
A Method of Estimating the Solution of a System
of Ordinary Differential Equations by Using Lemniscate
V. S. Zyuzin and N. A. Novikova 134
Author Index 135
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Reliable Computing. - 1997. - Vol. 3, No. 1.
Foreword 1 - 4
Inclusion of Zeros of Nowhere Differentiable
n-Dimensional Functions
Siegfried M. Rump 5 - 16
Sharpness in Interval Computations
Eldon R. Hansen 17 - 29
An Interval Algorithm for Bounding the Ranges
of Real-Valued Functions of One Real Variable
Michael A. Wolfe 31 - 50
NP-Hard Classes of Linear Algebraic Systems
with Uncertainties
Anatoly V. Lakeyev and Vladik Kreinovich 51 - 81
Use of Interval Slopes for the Irrational
Part of Factorable Functions
Lubomir V. Kolev 83 - 93
From Numerical Intervals to Set Intervals
(Interval-Related Results Presented at the
First International Workshop on Applications
and Theory of Random Sets)
Hung T. Nguyen and Vladik Kreinovich 95 - 102
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Reliable Computing. - 1997. - Vol. 3, No. 2.
Algebraic Approach in the ``Outer Problem''
for Interval Linear Equations
Sergey P. Shary 103 - 135
Numerical Verifications of Solutions for
Nonlinear Parabolic Equations in One-Space
Dimensional Case
Teruya Minamoto and Mitsuhiro T. Nakao 137 - 147
Is Solar System Stable? A Remark
Vladik Kreinovich and Andrew Bernat 149 - 154
Computing the Value of a Boolean Expression
with Interval Inputs is NP-Hard
Leticia S. Chee 155 - 172
Sign-Stable Solutions of Column-Vague
Linear Equation Systems
Josef Nedoma 173 - 180
Reviews Applications of Reliable
Scientific Computing 181 - 187
Information on New Textbooks 188 - 190
Interval-Related Talks at the 1996
International Workshop on
Control Mechanisms for Complex Systems 191 - 193
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Reliable Computing. - 1997. - Vol. 3, No. 3.
Foreword 195 - 198
Mathematical foundations and generalizations of interval arithmetic
S. Markov
Isomorphic Embeddings of Abstract Interval Systems 199 - 207
Z. Kulpa
Diagrammatic Representation of Interval Space in
Proving Theorems about Interval Relations 209 - 217
D. Berthelot and M. Daumas
Computing on Sequences of Embedded Intervals 219 - 227
J. Weinhofer and W. Haas
$H_\infty$-Control using Polynomial Matrices and
Interval Arithmetic 229 - 237
Numerical methods and computer assisted proofs
W. Hofschuster and W. Kraemer
A Computer Oriented Approach to Get
Sharp Reliable Error Bounds 239 - 248
W. Otten and W. Luther
Approximation Error and Error Accumulation
for the Landen Transform 249 - 258
C. Bliek
Fast Evaluation of Partial Derivatives
and Interval Slopes 259 - 268
O. Caprani, K. Madsen, and O. Stauning
Existence Test for Asynchronous Interval Iteration 269 - 275
M. Mrozek and M. Zelawski
Heteroclinic connections in the
Kuramoto-Sivashinsky equation:
a computer assisted proof 277 - 285
H.-J. Dobner and S. Ritter
Attacking a conjecture in mathematical physics
by combining methods of computational analysis
and scientific computing 287 - 295
B. Dobronets
Two-sided Multigrid Method
for Elliptic Boundary Value Problems 297 - 303
Complexity and constraint logic programming
B. Acioly and B. Bedregal
A Quasi-Metric Topology Compatible with
Inclusion Monotonicity on Interval Space 305 - 313
J. Rohn
Complexity of Some Linear Problems
with Interval Data 315 - 323
M. Rueher and C. Solnon
Concurent Cooperating Solvers on the Reals 325 - 333
F. Benhamou and L. Granvilliers
Automatic Generation of Numerical Redundancies
for Non-Linear Constraint Solving 335 - 344
Information
Interval'98
First announcement and call for papers 345 - 347
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Reliable Computing. - 1997. - Vol. 3, No. 4.
Slope Methods of Higher Order for the Inclusion
of Complex Roots of Polynomials
Ljiljana D. Petkovic, Slobodan Trickovic, and
Miodrag S. Petkovic 349 - 362
On Overestimations Produced by the Interval
Gaussian Algorithm (Dedicated to
Prof. Dr. Gerhard Heindl on the occasion
of his 60th birthday)
Jiri Rohn 363 - 368
Interval and Twin Arithmetics
Vyacheslav M. Nesterov 369 - 380
Finding Global Minima of Maximum Functions
by Using Exclusion Functions
without Derivatives
Ferenc Kalovics and Gabriella Meszaros 381 - 399
A New Approach to the Modal Regulator
Synthesis for Interval Plant with Scalar Input
Yelena M. Smagina 401 - 410
Error Reduction of the Taylor Centered Form
by Half and an Inner Estimation of the Range
Volker Stahl 411 - 420
How to Compute Interval Inclusions of
Geodetic Coordinates from
Interval Inclusions of Cartesian Coordinates
Gerhard Heindl 421 - 435
On a Theoretical Justification of the
Choice of Epsilon-Inflation in PASCAL-XSC
Vladik Kreinovich, Scott Starks,
and Guenter Mayer 437 - 445
Reviews:
Applications of Reliable Scientific Computing 447 - 452
Interval and Complexity Workshops Back-to-Back
with 1997 ACM Symposium on
Theory of Computing (STOC'97)
Luc Longpre and Martin Berz 453 - 457
Interval-Related Talks at NASA URC Conference
Monica Nogueira 459 - 460
Reliable Computing
Special Issue on Reliable Geometric Computations
Co-editors: H. Ratschek and J. Rokne 461 - 462
Best Paper Award to Zdzislaw Pawlak 463
Patrick Suppes is 75 464
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Reliable Computing. - 1998. - Vol. 4, No. 1.
Foreword 1 - 2
General numerical methods
Bounds for the Range of a Bivariate Polynomial
over a Triangle
Ralf Hungerbuehler and Juergen Garloff 3 - 13
An Interval Entropy Penalty Method for Nonlinear
Global Optimization
Huang Zhenyu 15 - 25
An Interval Polynomial Interpolation Problem
and Its Lagrange Solution
Chenyi Hu, Angelina Cardenas,
Stephanie Hoogendoorn, and Pedro Sepulveda Jr. 27 - 38
Algorithms That Still Produce a Solution
(Maybe Not Optimal) Even When Interrupted:
Shary's Idea Justified
Maria Beltran, Gilbert Castillo,
and Vladik Kreinovich 39 - 53
Applications
Interval Methods in Robot Navigation
David Morales and Tran Cao Son 55 - 61
Reliable Optimal Production Control with
Cobb-Douglas Model
Zhihui Huey Hu 63 - 69
Generalizations of interval computations
A Software Tool for Automatically Verified
Operations on Intervals and
Probability Distributions
Daniel Berleant, Hang Cheng 71 - 82
Computation and Application of Taylor
Polynomials with Interval Remainder Bounds
Martin Berz and Georg Hoffstaetter 83 - 97
Short communications
A New Application of Local Minima of
Interval Functions: Interval-Valued
Fuzzy Control
Clifton Davis 99 - 101
Intervals Help to Design an Imaging System
Graciela Gonzalez 103 - 104
Letters to the editor
A Brief Description of Gell-Mann's Lecture and
How Intervals May Help to Describe
Complexity in the Real World
Misha Koshelev and Luc Longpr'e 105 - 107
Intervals in Space-Time: A. D. Alexandrov is 85
Alexander Levichev and Olga Kosheleva 109 - 112
Information
Reliable Computing
Special Issue on Applications to Control,
Signals, and Systems 113 - 114
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Reliable Computing. - 1998. - Vol. 4, No. 2.
Mathematical Research
Constructive L^2 Error Estimates for Finite
Element Solutions of the Stokes Equations
Mitsuhiro T. Nakao, Nobito Yamamoto,
and Yoshitaka Watanabe 115 - 124
A New Method for Global Solution of Systems
of Non-Linear Equations
Lubomir V. Kolev 125 - 146
Bounding the Results of Arithmetic Operations
on Random Variables of Unknown Dependency
Using Intervals
Daniel Berleant and Chaim Goodman-Strauss 147 - 165
A Relation Between Morphological and
Interval Operations
Antony T. Popov 167 - 178
When Is the Product of Intervals Also
an Interval?
Olga Kosheleva and Piet G. Vroegindeweij 179 - 190
History of interval computations
Intervals and the Origins of Calculus
David Dennis, Vladik Kreinovich,
and Siegfried M. Rump 191 - 197
Short communication
One Criterion of Existence of a
Hamiltonian Cycle
Anatoly D. Plotnikov 199 - 202
Information
SCAN'97 203 - 204
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Reliable Computing. - 1998. - Vol. 4, No. 3.
Mathematical Research
On the Applicability of the Interval
Gaussian Algorithm
Guenter Mayer and Jiri Rohn 205 - 222
On a Second Derivative Test due to Qi
Michael A. Wolfe 223 - 234
Universal Approximation Theorem for
Interval Neural Networks
Mark R. Baker and Rajendra B. Patil 235 - 239
Applications
Estimating Uncertainties for Geophysical
Tomography
Diane I. Doser, Kevin D. Crain, Mark R. Baker,
Vladik Kreinovich, and Matthew C. Gerstenberger 241 - 268
The Use of Interval Analysis in
Hydrologic Systems
Tiraz R. Birdie and Karan S. Surana 269 - 281
An Application of Fuzzy Mathematical Morphology
to Interval-Valued Knowledge Representation:
A Remark
Antony T. Popov, Hung T. Nguyen, and
Leonid K. Reznik 283 - 290
Interval + Image = Wavelet:
For Image Processing under Interval Uncertainty,
Wavelets Are Optimal
Alejandro E. Brito and Olga Kosheleva 291 - 301
Short Communication
Exclusive OR Operation That Leads to the
Narrowest Intervals
Alfredo Gabaldon and Hung T. Nguyen 303 - 306
Review
Review of the book
O.Aberth: Precise Numerical Methods Using C++,
Academic Press, 1998 307 - 308
Information
International Conference Interval'98 309
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Reliable Computing. - 1998. - Vol. 4, No. 4.
Mathematical Research
Wrapping Effect and Wrapping Function
Roumen Anguelov and Svetoslav Markov 311 - 330
Reliable Collision Detection for
Time-Dependent Parametric Surfaces
Anthony Leclerc and Jeff Ely 331 - 344
An NP-Hardness Result for Nonlinear Systems
Christian Jansson 345 - 350
Optimal Enclosure of Quadratic Interval
Functions
Misha Koshelev, Luc Longpre, and
Patrick Taillibert 351 - 360
Verified Integration of ODEs and Flows
Using Differential Algebraic
Methods on High-Order Taylor Models
Martin Berz and Kyoko Makino 361 - 369
Application
A Note on Epsilon-Inflation
Siegfried M. Rump 371 - 375
Short Communications
Intersection Subdistributivity and
Interval Hull Superdistributivity
with Respect to the Interval Maps
Gregory G. Menshikov 377 - 381
Solving Linear Interval Systems Is NP-Hard
Even If We Exclude Overflow and Underflow
Gerhard Heindl, Vladik Kreinovich, and
Anatoly V. Lakeyev 383 - 388
Why Intervals? Because If We Allow Other Sets,
Tractable Problems Become Intractable
Monica Nogueira, Amarendra Nandigam 389 - 394
Letters to the editor
Hyper-Spectral Satellite Images:
Interval Methods May Be Helpful
Erzsebet Merenyi, Scott Starks, and
Karen Villaverde 395 - 397
Hilbert Problems (Almost) 100 Years Later
(From the Viewpoint of Interval Computations)
Olga M. Kosheleva 399 - 403
Review
Review of the book V. Kreinovich, A. Lakeyev,
J. Rohn, and P. Kahl,
Computational Complexity and Feasibility of
Data Procesing and Interval Computations.
Kluwer Academic Publishers, Dordrecht etc., 1998 405 - 409
Information
1998 SIAM Annual Meeting: Interval Highlights 411 - 412
ICRA99 International Conference on
Rational Approximation 413 - 414
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Reliable Computing. - 1999. - Vol. 5, No. 1.
Preface 1
Efficient Control of the Dependency Problem
Based on Taylor Model Methods
Kyoko Makino and Martin Berz 3 - 12
New Methods for High-Dimensional Verified
Quadrature
Martin Berz and Kyoko Makino 13 - 22
Solving Underdetermined Systems with Interval
Methods
Zhang Danqing, Li Weiguo and Shen Zuhe 23 - 33
Representing Knowledge within the Situation
Calculus Using Interval-Valued Epistemic Fluents
John Funge 35 - 61
How to Guarantee Finite Termination of Verifying
Global Optimization Codes
Gerhard Heindl 63 - 68
Expression Templates for Dot Product Expressions
Michael Lerch and Juergen Wolff von Gudenberg 69 - 80
Error Estimation for Indirect Measurements:
Interval Computation Problem Is (Slightly)
Harder Than a Similar Probabilistic Computational
Problem
Olga Kosheleva and Vladik Kreinovich 81 - 95
Information
NMA'98 97 - 100
SCAN'98 101 - 102
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Reliable Computing. - 1999. - Vol. 5, No. 2.
Mathematical Research
An Improved Method for Global Solution of
Non-Linear Systems
Lubomir V. Kolev 103 - 111
Rigorous Numerical Approach to Isolation in
Dynamical Systems on the Example of the
Kuramoto-Sivashinsky Equation
Marcin Zelawski 113 - 129
A Simple Derivation of the
Hansen-Bliek-Rohn-Ning-Kearfott Enclosure for
Linear Interval Equations
Arnold Neumaier 131 - 136
Computing Exact Bounds on Elements of an Inverse
Interval Matrix is NP-Hard
Gregory E. Coxson 137 - 142
Wrapping Function of the Initial Value Problem
for ODE: Applications
Roumen Anguelov 143 - 164
Estimation of Discrete-Event Systems Using
Interval Computation
Luc Jaulin, Jean-Louis Boimond, Laurent Hardouin 165 - 173
Application
Interval Estimates for Signal Processing:
Special Purpose Hardware
Olga Kosheleva, Sergio D. Cabrera,
Glenn A. Gibson, Sreedhar Cherukuri 175 - 196
Reviews
Interval Computations Help in Proving the
Kepler Conjecture 197 - 199
Review of the book "Bounded Queries
in Recursion Theory"
by W. I. Gasarch and G. A. Martin 201 - 203
Information
Karl Nickel is turned 75 205 - 206
Interval Workshop MISC'99 207 - 208
Reminiscences "Back in the Good Old Days..." 209
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Reliable Computing. - 1999. - Vol. 5, No. 3.
(Special Issue: Proceedings of the SCAN-98)
Guest editor: Tibor Csendes
Preface 211 - 212
Comparing Partial Consistencies
Helene Collavizza, Francois Delobel,
and Michel Rueher 213 - 228
Verified Computation of Fast Decreasing
Polynomials
Neli S. Dimitrova and Svetoslav M. Markov 229 - 240
An Accurate Distance-Calculation Algorithm
for Convex Polyhedra
Eva Dyllong, Wolfram Luther, and Werner Otten 241 - 253
Verified Error Bounds for Linear Systems
Through the Lanczos Process
Andreas Frommer and Andre Weinberg 255 - 267
A Representation of the Interval Hull of a
Tolerance Polyhedron Describing Inclusions
of Function Values and Slopes
Gerhard Heindl 269 - 278
A Few Results on Table-Based Methods
Jean-Michel Muller 279 - 288
An Interval Hermite-Obreschkoff Method for
Computing Rigorous Bounds on the Solution
of an Initial Value Problem for an Ordinary
Differential Equation
Nedialko S. Nedialkov and Kenneth R. Jackson 289 - 310
The Interval-Enhanced GNU Fortran Compiler
Michael J. Schulte, Vitaly Zelov, Ahmet Akkas,
and James Craig Burley 311 - 322
Outer Estimation of Generalized Solution Sets
to Interval Linear Systems
Sergey P. Shary 323 - 335
A Real Polynomial Decision Algorithm Using
Arbitrary-Precision Floating Point Arithmetic
Adam Strzebonski 337 - 346
A Numerical Verification Method of Solutions
for the Navier-Stokes Equations
Yoshitaka Watanabe, Nobito Yamamoto, and
Mitsuhiro T. Nakao 347 - 357
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Reliable Computing. - 1999. - Vol. 5, No. 4.
Mathematical Research
On the Componentwise Krawczyk-Moore Iteration
Kong Min, Liu Qi, and Shen Zuhe 359 - 370
On Discrete Minimax Problems in R Using
Interval Arithmetic
Michael A. Wolfe 371 - 383
Only Intervals Preserve the Invertibility of
Arithmetic Operations
Olga Kosheleva and Vladik Kreinovich 385 - 394
Solving Nonlinear Constrained Minimization
Problems with a New Interval Valued Function
Ferenc Kalovics 395 - 406
Applications
Synthesis of Robustly Stabilizing
General Order Compensators for
Interval Plants Using Interval Analysis
Paluri S. V. Nataraj and Suresh Srivastava 407 - 422
Reminiscences "Back in the Good Old Days..."
column edited by George F. Corliss
The Dawning
Ramon Moore 423 - 424
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Reliable Computing. - 2000. - Vol. 6, No. 1.
(Special issue on Reliable Geometric Computations)
Guest editors: Helmut Ratschek, Jon G. Rokne
Introduction to the Special Issue: What Can
One Learn from Box-Plane Intersections?
Helmut Ratschek and Jon G. Rokne 1 - 8
Robust and Efficient Ray Intersection of
Implicit Surfaces
Ole Caprani, Lars Hvidegaard,
Mikkel Mortensen, and Thomas Schneider 9 - 21
Correct Delaunay Triangulation in the Presence
of Inexact Inputs and Arithmetic
Jeffrey S. Ely and Anthony P. Leclerc 23 - 38
Exact Computation of Delaunay and
Power Triangulations
Marina Gavrilova, Helmut Ratschek, and Jon G. Rokne 39 - 60
Removing Degeneracies by Perturbing the Problem
or Perturbing the World
Pierre Alliez, Olivier Devillers, and Jack Snoeyink 61 - 79
Interval Constraint Plotting for Interactive
Visual Exploration of Implicitly Defined Relations
Timothy J. Hickey, Zhe Qiu, and Maarten H. van Emden 81 - 92
Reminiscences "Back in the Good Old Days..."
column edited by George F. Corliss
Interval Integration
L. B. Rall 93 - 94
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Reliable Computing. - 2000. - Vol. 6, No. 2.
The Hull of Preconditioned Interval Linear Equations
Eldon R. Hansen 95 - 103
Finding All Solutions of Nonlinear Equations
Using Linear Combinations of Functions
Kiyotaka Yamamura 105 - 113
Computation of the Bernstein Coefficients on
Subdivided Triangles
Ralf Hungerbuehler and Juergen Garloff 115 - 121
Jacobi and Gauss-Seidel Iterations for Polytopic
Systems: Convergence via Convex M-Matrices
Dusan M. Stipanovic and Dragoslav D. Siljak 123 - 137
A Coherence Space of Rational Intervals for a
Construction of IR
Gracaliz P. Dimuro, Antonio Carlos da R. Costa,
and Dalcidio M. Claudio 139 - 178
Interval Branch and Bound Algorithm for Finding
the First-Zero-Crossing-Point in One-Dimensional
Functions
Leocadio G. Casado, Inmaculada F. Garcia, and
Yaroslav D. Sergeyev 179 - 191
Accelerated Shift-and-Add Algorithms
Nathalie Revol and Jean-Claude Yakoubsohn 193 - 205
Mathematical Function Software on the Web - Are
Such Codes Useful for Verification Algorithms?
Werner Hofschuster and Walter Kraemer 207 - 218
Every Superinterval of the Function Range
Can Be an Interval-Computations Enclosure
Misha Koshelev 219 - 223
Reminiscences
Eldon R. Hansen 225
Erratum to:
A Simple Derivation of the
Hansen-Bliek-Rohn-Ning-Kearfott
Enclosure for Linear Interval Equations
(Reliable Computing Vol. 5 (2) (1999))
Arnold Neumaier 227
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Reliable Computing. - 2000. - Vol. 6, No. 3.
Special Issue on Applications to Control, Signals and Systems
Guest Editors: Juergen Garloff and Eric Walter
Foreword 229 - 230
Composite Interval Control Systems: Some Strong
Kharitonov-Like Properties
Long Wang 231 - 246
Nonconvex Polygon Interval Arithmetic as a Tool
for the Analysis and Design of
Robust Control Systems
Yuzo Ohta 247 - 279
Analysis of the Robustness of Predictive
Controllers via Modal Intervals
Josep Vehi, Jose Rodellar, Miguel Sainz, and
Joaquim Armengol 281 - 301
Application of Bernstein Expansion to the
Solution of Control Problems
Juergen Garloff 303 - 320
Interval Methods for Sinusoidal Parameter
Estimation: A Comparative Analysis
William W. Edmonson, Wen H. Lee, and
John M. M. Anderson 321 - 336
Robust Autonomous Robot Localization Using
Interval Analysis
Michel Kieffer, Luc Jaulin, Eric Walter, and
Dominique Meizel 337 - 361
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Reliable Computing. - 2000. - Vol. 6, No. 4.
Special Issue:
Proceedings of the International Conference on Rational Approximation
ICRA'99, June 6-11, 1999, Antwerp, Belgium
Guest Editor: Brigitte Verdonk
Foreword 363
Effective Computation of Rational Approximants
and Interpolants
Bernhard Beckermann and George Labahn 365 - 390
Rational Interpolation from Stochastic Data:
A New Froissart's Phenomenon
Jean-Daniel Fournier and Maciej Pindor 391 - 409
Reliability of Lanczos-Type Product Methods
from Perturbation Theory
Peter R. Graves-Morris 411 - 428
Hybrid Rational Function Approximation and
Its Accuracy Analysis
Hiroshi Kai and Matu-Tarow Noda 429 - 438
Numerical Computation of the Least Common
Multiple of a Set of Polynomials
Nicos Karcanias and Marilena Mitrouli 439 - 457
On Factorization of Analytic Functions and
Its Verification
Tetsuya Sakurai and Hiroshi Sugiura 459 - 470
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Reliable Computing. - 2001. - Vol. 7, No. 1.
Mathematical Research
Path Planning Using Intervals and Graphs
Luc Jaulin 1 - 15
Automatic Computation of a Linear
Interval Enclosure
Lubomir V. Kolev 17 - 28
On Kernel Inclusions
Hans-Juergen Dobner 29 - 39
Roundoff-Free Number Fields for
Interval Computations
Vladik Kreinovich 41 - 47
Short Communications
A Note on a Uniqueness Theorem for the
Second-Derivative Test of Qi
Michael A. Wolfe 49 - 52
On /\-Subdistributivity and \/-Superdistributivity
with Respect to Interval Map in Kaucher Arithmetic
Gregory G. Menshikov, Alexey V. Tomashevsky 53 - 57
The Feasibility of the Interval Gaussian
Algorithm for Arrowhead Matrices
Uwe Schaefer 59 - 62
Reminiscences "Back in the Good Old Days"
The Mystery of Intervals
Svetoslav Markov 63 - 65
Information
Interval Methods and Their Applications:
invited sessions at the World Automation
Congress (WAC'2000) 67 - 68
Session "Interval and Computer-Algebraic Methods
in Science and Engineering" at the 6th
International Association for Mathematics and
Computers in Simulation (IMACS) Conference on
Applications of Computer Algebra (ACA'2000) 69 - 70
A special session on Granular Computing and
Interval Computations at the 19th International
Conference of the North American Fuzzy Information
Processing Society (NAFIPS) 71 - 72
Minisymposium on Applications of Interval
Computations at the Third World Congress of
Nonlinear Analysts 73 - 74
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Reliable Computing. - 2001. - Vol. 7, No. 2.
Foreword 75
Modal Intervals
Ernest Gardenes, Miguel A. Sainz, Lambert Jorba,
Remei Calm, Rosa Estela, Honorino Mielgo,
and Albert Trepat 77 - 111
On the Algebraic Properties of Intervals
and Some Applications
Svetoslav Markov 113 - 127
Multiplication Distributivity of Proper
and Improper Intervals
Evgenija D. Popova 129 - 140
Interval Gauss-Seidel Method for Generalized
Solution Sets to Interval Linear Systems
Sergey P. Shary 141 - 155
A Limitation for Underestimation via
Twin Arithmetic
Peter Hertling 157 - 169
Application of Modal Intervals to the
Generation of Error-Bounded Envelopes
Joaquim Armengol, Josep Vehi,
Louise Trave-Massuyes, and Miguel Angel Sainz 171 - 185
Information
SCAN 2000: GAMM-IMACS International Symposium
on Scientific Computing, Computer Arithmetic,
and Validated Numerics
Interval 2000: International Conference on
Interval Methods in Science and Engineering 187 - 191
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Reliable Computing. - 2001. - Vol. 7, No. 3.
Foreword 193 - 194
Mathematical Research
On Bounding Solutions of Underdetermined Systems
Michael A. Wolfe 195 - 207
On The Theory of Error Control Based on
Moduli with Common Factors
Andraos Sweidan, Amman, Jordan, and Ahmad A. Hiasat 209 - 218
Robust Control Using Interval Analysis
Vladimir N. Shashikhin 219 - 230
Reliable Minimax Parameter Estimation
Luc Jaulin 231 - 246
Spigot Algorithm and Root Computing
Dang-Khoa Do 247 - 273
Short Communication
A Comment on the Shape of the Solution Set for
Systems of Interval Linear Equations with
Dependent Coefficients
Goetz Alefeld, Vladik Kreinovich, Guenter Mayer,
and Michael Huth 275 - 277
Information
Interval talks at the International Conference
on Intelligent Technologies InTech'2000 279 - 280
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Reliable Computing. - 2001. - Vol. 7, No. 4.
Mathematical Research
Synchronous and Asynchronous Interval
Newton-Schwarz Methods for a Class of
Large Systems of Nonlinear Equations
Hartmut Schwandt 281 - 306
Validated Bounds for Taylor Coefficients of
Analytic Functions
Markus Neher 307 - 319
Computer Implementation
Automatic Forward Error Analysis for
Floating Point Algorithms
Walter Kraemer and Armin Bantle 321 - 340
Application
Interval Methods in Non-Destructive Testing
of Material Structures
Keith Worden, Roberto Osegueda, Carlos Ferregut,
Soheil Nazarian, Debra L. George, Mary J. George,
Vladik Kreinovich, Olga Kosheleva,
and Sergio Cabrera 341 - 352
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Reliable Computing. - 2001. - Vol. 7, No. 5.
Mathematical Research
Idempotent Interval Analysis and
Optimization Problems
Grigori L. Litvinov and Andrei N. Sobolevskii 353 - 377
Verified High-Order Inversion of Functional
Dependencies and Interval Newton Methods
Martin Berz and Jens Hoefkens 379 - 398
Cheap and Tight Bounds on the Solution Set of
Perturbed Systems of Nonlinear Equations
Lubomir V. Kolev and Ivo P. Nenov 399 - 408
On Maximal Inner Estimation of the Solution
Sets of Linear Systems with Interval Parameters
Irene A. Sharaya 409 - 424
Short Communications
An Example of Singularity in Nonlinear Systems
R. Baker Kearfott 425 - 429
Claude E. Shannon (1916-2001) 431 - 432
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Reliable Computing. - 2001. - Vol. 7, No. 6.
Mathematical Research
Linear Interval Tolerance Problem and
Linear Programming Techniques
Oliver Beaumont and Bernard Philippe 433 - 447
An Effective High-Order Interval Method for
Validating Existence and Uniqueness of the
Solution of an IVP for an ODE
Nedialko S. Nedialkov, Kenneth R. Jackson,
and John D. Pryce 449 - 465
On the Combination of Interval Constraint Solvers
Laurent Granvilliers 467 - 483
The Preliminary Enclosing of the ODE Solutions
on the Base of the Cauchy-Duhamel Identity
Gregory G. Menshikov 485 - 495
A Surprising Approach in Interval
Global Optimization
Sergey P. Shary 497 - 505
Information
Gregory G. Menshikov has turned 70 507 - 508
SCAN 2002 509 - 510
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Reliable Computing. - 2002. - Vol. 8, No. 1.
Mathematical Research
Two Ways to Extend the Cholesky Decomposition to
Block Matrices with Interval Entries
Uwe Schaefer 1 - 20
Approximate Quantified Constraint Solving by
Cylindrical Box Decomposition
Stefan Ratschan 21 - 42
Exact Minkowski Products of N Complex Disks
Rida T. Farouki, Helmut Pottmann 43 - 66
Verification of Invertibility of Complicated
Functions over Large Domains
Jens Hoefkens, Martin Berz 67 - 82
A New Subdivision Strategy for Range Computations
Paluri S. V. Nataraj, Suresh Mandir Sheela 83 - 92
Information
Special Issue on the Linkages Between Interval
Mathematics and Fuzzy Set Theory 93 - 95
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Reliable Computing. - 2002. - Vol. 8, No. 2.
Mathematical Research
Interval-Valued Finite Markov Chains
Igor O. Kozine and Lev V. Utkin 97 - 113
Sharp Bounds on Interval Polynomial Roots
Eldon R. Hansen and G. William Walster 115 - 122
Algorithms and Computations
A Parallelized Version of the Covering Algorithm
for Solving Parameter-Dependent Systems of
Nonlinear Equations
Paluri S. V. Nataraj and Airani Kalathil Prakash 123 - 130
Interval Computation of Viswanath's Constant
Joao Batista Oliveira and Luiz Henrique
de Figueiredo 131 - 138
Applications and Tools
Efficient Interval Linear Equality Solving in
Constraint Logic Programming
Chong-Kan Chiu and Jimmy Ho-Man Lee 139 - 174
Information
Reliable Computing: Special Issue on Dependable
Reasoning about Uncertainty
Daniel Berleant 175 - 176
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Reliable Computing. - 2002. - Vol. 8, No. 3.
Mathematical Research
Bounding Perturbations in Zeros of Nonlinear
Systems
Michael A. Wolfe 177 - 188
Formal Solution to Systems of Interval Linear
or Non-Linear Equations
Miguel A. Sainz, Ernest Gardenyes, and
Lambert Jorba 189 - 211
In Case of Interval (or More General) Uncertainty,
No Algorithm Can Choose the Simplest Representative
Gerhard Heindl, Vladik Kreinovich, and Maria Rifqi 213 - 227
An Approach to Overcome Division by Zero in the
Interval Gauss Algorithm
Jan Mayer 229 - 237
Intervals of Inverse M-matrices
Charles R. Johnson and Ronald L. Smith 239 - 243
Short communication
Rump's Example Revisited
Eugene Loh and G. William Walster 245 - 248
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Reliable Computing. - 2002. - Vol. 8, No. 4.
Mathematical Research
Sparse Systems in Fixed Point Form
Ramon E. Moore 249 - 265
On Existence and Uniqueness Verification for
Non-Smooth Functions
R. Baker Kearfott 267 - 282
Interval Estimations of Solution Sets to
Real-Valued Systems of Linear
or Non-Linear Equations
Miguel A. Sainz, Ernest Gardenyes, and Lambert Jorba 283 - 305
Short Communication
Interval Arithmetic on Multimedia Architectures
Juergen Wolff von Gudenberg 307 - 312
Letter to the Editor
Grand Challenges and Scientific Standards in
Interval Analysis
Arnold Neumaier 313 - 320
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Reliable Computing. - 2002. - Vol. 8, No. 5.
Mathematical Research
A New Technique in Systems Analysis under
Interval Uncertainty and Ambiguity
Sergey P. Shary 321 - 418
Information
SIAM Conference on Optimization,
Validated Computing 2002, and the
Fields Institute Informal Working Group on
Validated Optimization 419 - 424
Interval-Related Talks at the Annual Conference
of the North American Fuzzy Information
Processing Society NAFIPS'02 425 - 426
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Reliable Computing. - 2002. - Vol. 8, No. 6.
Mathematical Research
A QFT Procedure for Generating Design Frequencies
and Bounds of Guaranteed Accuracy
Paluri S. V. Nataraj and Suresh Mandir Sheela 427 - 451
Symbolic Preconditioning with Taylor Models:
Some Examples
R. Baker Kearfott and G. William Walster 453 - 468
Kernel-Splitting Technique for Enclosing the
Solution of Fredholm Equations of the First Kind
Hans-Juergen Dobner 469 - 479
Range Estimation Is NP-Hard for e^2 Accuracy and
Feasible for e^(2-d)
Vladik Kreinovich 481 - 491
Outer Solution of Linear Systems Whose Elements
Are Affine Functions of Interval Parameters
Lubomir V. Kolev 493 - 501
Information
Epistemic Uncertainty Workshop 503 - 505
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Reliable Computing. - 2003. - Vol. 9, No. 1.
Mathematical Research
Diagrammatic Analysis of Interval Linear
Equations: Part I: Basic Notions and the
One-Dimensional Case
Zenon Kulpa 1 - 20
Controlling the Wrapping Effect in the Solution
of ODEs for Asteroids
Jens Hoefkens, Martin Berz, and Kyoko Makino 21 - 41
Review
Taylor Forms - Use and Limits
Arnold Neumaier 43 - 79
Information
COCOS'02: A Workshop on Global Constrained
Optimization and Constraint Satisfaction
R. Baker Kearfott 81 - 87
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Reliable Computing. - 2003. - Vol. 9, No. 2.
Special Issue:
Proceedings of the Validated Computing 2002 conference,
May 23-25, 2002, Toronto, Canada
Guest Editor: R. Baker Kearfott
Preface 89 - 90
Statool: A Tool for Distribution Envelope
Determination (DEnv), an Interval-Based Algorithm for
Arithmetic on Random Variables
Daniel Berleant, Lizhi Xie, Jianzhong Zhang 91 - 108
Numerical Experiences with a New Generalized
Subinterval Selection Criterion for Interval Global
Optimization
Tibor Csendes 109 - 125
Estimating and Validating the Cumulative Distribution
of a Function of Random Variables: Toward the
Development of Distribution Arithmetic
Weldon A. Lodwick, K. David Jamison 127 - 141
Interval Methods for Accelerated Global Search
in the Microsoft Excel Solver
Ivo P. Nenov, Daniel H. Fylstra 143 - 159
Robust Approximation of Offsets, Bisectors, and
Medial Axes of Plane Curves
Joao Batista Oliveira, Luiz Henrique de Figueiredo 161 - 175
Evaluation of Functions, Gradients, and Jacobians
Louis B. Rall 177 - 182
Information
SCAN'2002 183 - 184
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Reliable Computing. - 2003. - Vol. 9, No. 3.
Mathematical Research
Higher Order Convergence for Multidimensional
Functions with a New Taylor-Bernstein Form as
Inclusion Function
Paluri S. V. Nataraj, Ketan Kotecha 185 - 203
Diagrammatic Analysis of Interval Linear Equations.
Part II: The Two-Dimensional Case and Generalization
to n Dimensions
Zenon Kulpa 205 - 228
Computation of Sharp Rigorous Componentwise Error
Bounds for the Approximate Solutions of Systems of
Linear Equations
Takeshi Ogita, Shin'ichi Oishi, Yasunori Ushiro 229 - 239
Letter to the editor
Finding All Solution Sets of Piecewise-Trapezoidal
Equations Described by Set-Valued Functions
Kiyotaka Yamamura 241 - 250
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Reliable Computing. - 2003. - Vol. 9, No. 4.
Mathematical Research
Worst-Case Simulation of Discrete Linear
Time-Invariant Interval Dynamic Systems
Vicenc Puig, Jordi Saludes, and Joseba Quevedo 251 - 290
Optimal Bicentered Form
Youkang Fang 291 - 302
Asymptotic Stability of Interval Time-Delay Systems
Svetlana P. Sokolova and Ruslan S. Ivlev 303 - 313
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Reliable Computing. - 2003. - Vol. 9, No. 5.
Special Issue:
Proceedings of the Validated Computing 2002 conference,
May 23-25, 2002, Toronto, Canada
Guest Editor: R. Baker Kearfott
Preface 315
Interval Global Optimization in Solvent Design
Luke E. K. Achenie and Manish Sinha 317 - 338
Extended Interval Power Function
Walter Kraemer and Juergen Wolff von Gudenberg 339 - 347
Are There Easy-to-Check Necessary and Sufficient
Conditions for Straightforward Interval Computations
To Be Exact?
Vladik Kreinovich, Luc Longpre, and James J. Buckley 349 - 358
Some Computer Assisted Proofs for Solutions of
the Heat Convection Problems
Mitsuhiro T. Nakao, Yoshitaka Watanabe,
Nobito Yamamoto, and Takaaki Nishida 359 - 372
Reliable Computation of Frequency Response Plots
for Nonrational Transfer Functions to
Prescribed Accuracy
Paluri S. V. Nataraj and Jayesh J. Barve 373 - 389
Accelerated Enclosure Methods for Ordinary Free
Boundary Problems
Uwe Schaefer 391 - 403
Information
Interval-Related Talks at the 2003 IEEE
International Conference on Fuzzy Systems 405 - 406
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Reliable Computing. - 2003. - Vol. 9, No. 6.
Special Issue on Dependable Reasoning about
Uncertainty
Guest Editor: Daniel Berleant
Dependable Handling of Uncertainty
Daniel Berleant, Mei-Peng Cheong, Chris Chu,
Yong Guan, Ahmed Kamal, Gerald Sheble,
Scott Ferson, and James F. Peters 407 - 418
Computation of Bounds on Population Parameters When
the Data Are Incomplete
Joel L. Horowitz, Charles F. Manski,
Maria Ponomareva, and Joerg Stoye 419 - 440
Exact Upper Bound on the Mean of the Product
of Many Random Variables with Known Expectations
Vladik Kreinovich, Scott Ferson, and Lev Ginzburg 441 - 463
Convex Imprecise Previsions
Renato Pelessoni and Paolo Vicig 465 - 485
Tree-Based Credal Networks for Classification
Marco Zaffalon and Enrico Fagiuoli 487 - 509
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Reliable Computing. - 2004. - Vol. 10, No. 1.
Mathematical Research
Set Computation for Nonlinear Control
Luc Jaulin, Stefan Ratschan, and Laurent Hardouin 1 - 26
Global Optimization with Higher Order
Inclusion Function Forms.
Part 1: A Combined Taylor-Bernstein Form
Paluri S. V. Nataraj and Ketan Kotecha 27 - 44
On the Significance of Digits in Interval Notation
Maarten H. van Emden 45 - 58
Information
Special Session "Set-Valued Numerics and
Reliable Computing" 59 - 61
Interval-Related Talks at the 4th International
Conference on Frontiers in Global Optimization 63 - 70
Interval-Related Talks at the 22th International
Conference of the North American Fuzzy Information
Processing Society NAFIPS'03 71 - 73
Computability and Complexity in Analysis (CCA).
A View from Interval Computations 75 - 80
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Reliable Computing. - 2004. - Vol. 10, No. 2.
Special Issue: Dependable Reasoning about Uncertainty
Guest Editor: D. Berleant
Introduction 81 - 82
Dirty Pages of Logarithm Tables, Lifetime of the
Universe, and (Subjective) Probabilities on
Finite and Infinite Intervals
Hung T. Nguyen, Vladik Kreinovich, and Luc Longpre 83 - 106
On the Use of Random Set Theory to Bracket
the Results of Monte Carlo Simulations
Fulvio Tonon 107 - 137
Using Pearson Correlation to Improve Envelopes
around the Distributions of Functions
Daniel Berleant and Jianzhong Zhang 139 - 161
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Reliable Computing. - 2004. - Vol. 10, No. 3.
Mathematical Research
Slope Intervals, Generalized Gradients,
Semigradients, Slant Derivatives, and Csets
Humberto Munoz and R. Baker Kearfott 163 - 193
Integral Approximation of Rays and Verification
of Feasibility
Waltraud Huyer and Arnold Neumaier 195 - 207
On a Refined Analysis of Some Problems in
Interval Arithmetic Using Real Number
Complexity Theory
Klaus Meer 209 - 225
A Method for Outer Interval Solution of
Linear Parametric Systems
Lubomir V. Kolev 227 - 239
Letter to the Editor
Fast Multiplication of Interval Matrices
(Interval Version of Strassen's Algorithm)
Martine Ceberio and Vladik Kreinovich 241 - 243
Information
Interval-Related Talks at InTech'03 245 - 246
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Reliable Computing. - 2004. - Vol. 10, No. 4.
Special Issue on Interval Analysis and Fuzzy Sets
Guest Editor: Weldon A. Lodwick
Introduction 247 - 248
Clouds, Fuzzy Sets, and Probability Intervals
Arnold Neumaier 249 - 272
Probability-Possibility Transformations,
Triangular Fuzzy Sets, and
Probabilistic Inequalities
Didier Dubois, Laurent Foulloy, Gilles Mauris,
and Henri Prade 273 - 297
Characterization of Interval Fuzzy Logic Systems
of Connectives by Group Transformations
Ladislav J. Kohout and Eunjin Kim 299 - 334
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Reliable Computing. - 2004. - Vol. 10, No. 5.
Special Issue on Interval Analysis and Fuzzy Sets
Guest Editor: Weldon A. Lodwick
Introduction 247 - 248
Modeling Uncertain Sparse Data with Fuzzy B-splines
Angelo Marcello Anile and Salvatore Spinella 335 - 355
Fuzzy Linear Programming with Interactive
Uncertain Parameters
Masahiro Inuiguchi and Tetsuzo Tanino 357 - 367
Application of Functional Intervals to the
Response Evaluation of Linear Time-Invariant
Systems with Fuzzy Input
Jorge Bondia and Jesus Pico 369 - 387
Solutions for the Portfolio Selection Problem with
Interval and Fuzzy Coefficients
Masaaki Ida 389 - 400
Eliminating Duplicates under Interval and
Fuzzy Uncertainty: An Asymptotically Optimal
Algorithm and Its Geospatial Applications
Roberto Torres, G. Randy Keller, Vladik Kreinovich,
Luc Longpre, and Scott A. Starks 401 - 422
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Reliable Computing. - 2004. - Vol. 10, No. 6.
Enclosing Solutions of Linear Complementarity
Problems for H-matrices
Goetz Alefeld, Zhengyu Wang, and Zuhe Shen 423 - 435
Ostrowski-like Method with Corrections for the
Inclusion of Polynomial Zeros
Miodrag S. Petkovic and Dusan M. Milosevic 437 - 467
Discrete Optimization Problems with Interval Data:
Pareto Set of Solutions or Set of Weak Solutions?
Galina Kozina 469 - 487
Spigot Algorithm and Reliable Computation of
Natural Logarithm
Dang-Khoa Do 489 - 500
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Reliable Computing. - 2005. - Vol. 11, No. 1.
Mathematical Research
Contracting Optimally an Interval Matrix without
Loosing Any Positive Semi-Definite Matrix Is a
Tractable Problem
Luc Jaulin and Didier Henrion 1 - 17
Computing System Reliability Given Interval-Valued
Characteristics of the Components
Lev V. Utkin and Igor O. Kozine 19 - 34
A Normal Form Supplement to the
Oettli-Prager Theorem
Jiri Rohn 35 - 39
Interval Schemes for Singularly Perturbed
Initial Value Problems
Abdelhay A. Salama and Emad Hamdy 41 - 58
Outlier Detection under Interval Uncertainty:
Algorithmic Solvability and Computational Complexity
Vladik Kreinovich, Luc Longpre, Praveen Patangay,
Scott Ferson, and Lev Ginzburg 59 - 76
On the Proofs of Some Statements Concerning
the Theorems of Kantorovich, Moore, and Miranda
Marco Schnurr 77 - 85
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Reliable Computing. - 2005. - Vol. 11, No. 2.
Mathematical Research
On the Solutions of the Interval System
[x]=[A][x]+[b]
Hans-Robert Arndt and Guenter Mayer 87 - 103
The Optimal Solution of an Interval System of
Linear Algebraic Equations
Marina Lyashko 105 - 127
Linear Interval Equations: Midpoint
Preconditioning May Produce a 100% Overestimation
for Arbitrarily Narrow Data Even in Case n=4
Jiri Rohn 129 - 135
Application
Using Zonotopes for Overestimation-Free
Interval Least-Squares --
Some Geodetic Applications
Steffen Schoen and Hansjoerg Kutterer 137 - 155
Information
SCAN'2004
11th GAMM-IMACS International Symposium on
Scientific Computing, Computer Arithmetic,
and Validated Numerics 157 - 159
Second R. E. Moore Prize Awarded at SCAN'2004 161 - 162
Errata and Opinion to: "An Interval Entropy
Penalty Method for Nonlinear Global
Optimization," by Zhenyu Huang,
Reliable Computing 4 (1) (1998)
R. Baker Kearfott 163 - 164
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Reliable Computing. - 2005. - Vol. 11, No. 3.
Mathematical Research
Enclosing Solutions of Singular Interval Systems
Iteratively
Goetz Alefeld and Guenter Mayer 165 - 190
Fast Inclusion of Interval Matrix Multiplication
Takeshi Ogita and Shin'ichi Oishi 191 - 205
Exact Bounds on Finite Populations of Interval Data
Scott Ferson, Lev Ginzburg, Vladik Kreinovich,
Luc Longpre, and Monica Aviles 207 - 233
Tolerances in Geometric Constraint Problems
Johannes Wallner, Hans-Peter Schroecker,
and Shi-Min Hu 235 - 251
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Reliable Computing. - 2005. - Vol. 11, No. 4.
Mathematical Research
Empirical Investigation of the Convergence Speed
of Inclusion Functions in a Global
Optimization Context
Boglarka Toth and Tibor Csendes 253 - 273
Applications and Tools
Motivations for an Arbitrary Precision Interval
Arithmetic and the MPFI Library
Nathalie Revol and Fabrice Rouillier 275 - 290
Checking If There Exists a Monotonic Function
That Is Consistent with the Measurements:
An Efficient Algorithm
Kavitha Tupelly, Vladik Kreinovich,
and Karen Villaverde 291 - 312
A Constructive Criticism of the C/C++ Proposal
for Complex Arithmetic
Franky Backeljauw and Annie Cuyt 313 - 319
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Reliable Computing. - 2005. - Vol. 11, No. 5.
Special Issue: Selected works presented at the International
Workshop on Interval Mathematics and Constraint Propagation Methods
June 23-24, 2004, Akademgorodok, Novosibirsk, Russia
Guest Editor: Sergey P. Shary
Preface 321 - 322
Interval-Affine Gaussian Algorithm for
Constrained Systems
Ramil R. Akhmerov 323 - 341
Developing Interval Global Optimization Algorithms
on the Basis of Branch-and-Bound and Constraint
Propagation Methods
Yuri G. Dolgov 343 - 358
Interval Mathematical Library Based on Chebyshev
and Taylor Series Expansion
Alexei G. Ershov and Tamara P. Kashevarova 359 - 367
Quantified Set Inversion Algorithm
with Applications to Control
Pau Herrero, Miguel A. Sainz, Josep Vehi,
and Luc Jaulin 369 - 382
Validated Constraint Solving - Practicalities,
Pitfalls, and New Developments
R. Baker Kearfott 383 - 391
An Interval Global Optimization Algorithm
Combining Symbolic Rewriting and Componentwise
Newton Method Applied to Control a Class
of Queueing Systems
Bartlomiej Jacek Kubica and Krzysztof Malinowski 393 - 411
Boundary Realizations Method for Interval Linear
Dynamic Systems
Sergey G. Pushkov and Svetlana Yu. Kalinkina 413 - 423
On Unbounded Tolerable Solution Sets
Irene A. Sharaya 425 - 432
On Fitting Empirical Data under Interval Error
Sergei I. Zhilin 433 - 442
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Reliable Computing. - 2005. - Vol. 11, No. 6.
Mathematical Research
A Right-Preconditioning Process for the
Formal-Algebraic Approach to Inner and Outer
Estimation of AE-Solution Sets
Alexandre Goldsztejn 443 - 478
Optimal Finite Characterization of Linear
Problems with Inexact Data
Vladik Kreinovich 479 - 489
Short Communications
How Strong Is Strong Regularity?
Jiri Rohn 491 - 493
A Theorem on Regularity of Interval Matrices
Eldon Hansen 495 - 497
Information
Reliable Computations and Their Applications 499 - 503
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Reliable Computing. - 2006. - Vol. 12, No. 1.
Mathematical Research
Complex Interval Arithmetic Using Polar Form
Yves Candau, Tarek Raissi, Nacim Ramdani,
and Laurent Ibos 1 - 20
Sharpening Interval Computations
Eldon Hansen 21 - 34
Interval Householder Method for Complex Linear
Systems
Bakyt S. Djanybekov 35 - 43
Applications
Robust Control for Two-Time-Scale Discrete
Interval Systems
Balasaheb M. Patre and Bijnan Bandyopadhyay 45 - 58
Fast Algorithm for Computing the Upper Endpoint
of Sample Variance for Interval Data: Case of
Sufficiently Accurate Measurements
Gang Xiang 59 - 64
Information
Los Alamos National Laboratory Uncertainty
Workshop: An Interval Perspective 65 - 71
Towards Real World Applications: Interval-Related
Talks at NAFIPS'05 73 - 77
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Reliable Computing. - 2006. - Vol. 12, No. 2.
Mathematical Research
A Contribution to the Feasibility of the
Interval Gaussian Algorithm
Guenter Mayer 79 - 98
Regularity of Interval Matrices and Theorems of
the Alternatives
Jiri Rohn 99 - 105
A Method for Outer Interval Solution of Systems of
Linear Equations Depending Linearly on Interval
Parameters
Iwona Skalna 107 - 120
Outer Interval Solution of the Eigenvalue Problem
under General Form Parametric Dependencies
Lubomir V. Kolev 121 - 140
Applications
Efficient Task Scheduling in the Parallel
Result-Verifying Solution of Nonlinear Systems
Thomas Beelitz, Bruno Lang, and
Christian H. Bischof 141 - 151
Information
Dealing with Imprecise Probabilities:
Interval-Related Talks at ISIPTA'05 153 - 165
Second Scandinavian Workshop on Interval Methods
and Their Applications 167 - 169
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Reliable Computing. - 2006. - Vol. 12, No. 3.
Mathematical Research
A General Reliable Quadratic Form:
An Extension of Affine Arithmetic
Frederic Messine and Ahmed Touhami 171 - 192
Improvement of a Direct Method for Outer
Solution of Linear Parametric Systems
Lubomir V. Kolev 193 - 202
Geometric Constructions with Discretized
Random Variables
Hans-Peter Schroecker and Johannes Wallner 203 - 223
Hardware
Hardware Support for Interval Arithmetic
Reinhard Kirchner and Ulrich W. Kulisch 225 - 237
Short Communication
Solving Overdetermined Systems of Interval
Linear Equations
Eldon Hansen and G. William Walster 239 - 243
Letter to the Editor
Jiri Rohn 245 - 246
Information
Interval-Related Talks at the International
Conference on Fuzzy Systems, Neural Networks,
and Genetic Algorithms FNG'05 247 - 251
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Reliable Computing. - 2006. - Vol. 12, No. 4.
Mathematical Research
A Multidimensional Interval Newton Method
Eldon Hansen 253 - 272
Population Variance under Interval Uncertainty:
A New Algorithm
Evgeny Dantsin, Vladik Kreinovich,
Alexander Wolpert, and Gang Xiang 273 - 280
New Formulae for Multiplication of Intervals
Lubomir V. Kolev 281 - 292
Applications
Modelling Geometric Objects and Tolerances
with Intervals: Data Exchange with ISO Standard
STEP
Eva Dyllong, Wolfram Luther, and Holger Traczinski 293 - 302
Computational Experience with Rigorous Error Bounds
for the Netlib Linear Programming Library
Christian Keil and Christian Jansson 303 - 321
Robust Plotting of Polar Algebraic Curves, Space
Algebraic Curves, and Offsets of Planar
Algebraic Curves
Huahao Shou, Jie Shen, and David Yoon 323 - 335
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Reliable Computing. - 2006. - Vol. 12, No. 5.
Mathematical Research
The Set of Hausdorff Continuous Functions - The
Largest Linear Space of Interval Functions
Roumen Anguelov, Svetoslav Markov,
and Blagovest Sendov 337 - 363
Towards Optimal Use of Multi-Precision Arithmetic:
A Remark
Vladik Kreinovich and Siegfried Rump 365 - 369
Applications
Analysis and Design of Robust Controllers Using
the Interval Diophantine Equation
Alfredo D. S. Lordelo, Edvaldo A. Juzzo,
and Paulo A. V. Ferreira 371 - 388
Parameter Reconstruction for Biochemical Networks
Using Interval Analysis
Warwick Tucker and Vincent Moulton 389 - 402
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Reliable Computing. - 2006. - Vol. 12, No. 6.
Special Issue on Reliable Engineering Computing
Guest Editors: Rafi L. Muhanna and Robert L. Mullen
Preface 403 - 404
Introductory Remarks on Reliable Engineering
Computing
Ramon E. Moore 405 - 408
Handling Uncertainty in the Development and Design
of Chemical Processes
David B. Johnson and I. David L. Bogle 409 - 426
Reliable Modeling and Optimization for Chemical
Engineering Applications: Interval Analysis
Approach
Youdong Lin, C. Ryan Gwaltney, and
Mark A. Stadtherr 427 - 450
Uncertainty in Thermal Basin Modeling:
An Interval Finite Element Approach
Sebastiao C. Pereira, Ulisses T. Mello,
Nelson F. F. Ebecken, and Rafi L. Muhanna 451 - 470
Towards Combining Probabilistic and Interval
Uncertainty in Engineering Calculations:
Algorithms for Computing Statistics under
Interval Uncertainty, and Their
Computational Complexity
Vladik Kreinovich, Gang Xiang, Scott A. Starks,
Luc Longpr'e, Martine Ceberio, Roberto Araiza,
Jan Beck, Raj Kandathi, Asis Nayak,
Roberto Torres, and Janos G. Hajagos 471 - 501
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Reliable Computing. - 2007. - Vol. 13, No. 1.
Special Issue on Reliable Engineering Computing
Guest Editors: Rafi L. Muhanna and Robert L. Mullen
Experiments with Range Computations Using
Extrapolation
Nataraj S. V. Paluri and Shanta Sondur 1 - 23
Monte-Carlo-Type Techniques for Processing
Interval Uncertainty, and Their Potential
Engineering Applications Vladik Kreinovich,
Jan Beck, Carlos Ferregut, Araceli Sanchez,
G. Randy Keller, Matthew Averill, and
Scott A. Starks 25 - 69
Interval Monte Carlo as an Alternative to
Second-Order Sampling for Estimating Ecological
Risk
Janos G. Hajagos 71 - 81
Requirements Analysis for Engineering
Computation: A Systematic Approach for
Improving Reliability
Spencer Smith, Lei Lai, and Ridha Khedri 83 - 107
Information
Interval-Related Talks at the North American
Fuzzy Information Processing Society
Annual Conference NAFIPS'06 109 - 111
Interval-Related Talks at the Second
International Conference on Fuzzy Sets and
Soft Computing in Economics and Finance 113 - 117
Interval Talks at the International Conference
on Information Processing and Management of
Uncertainty in Knowledge-Based Systems IPMU'2006 119 - 124
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Reliable Computing. - 2007. - Vol. 13, No. 2.
Special Issue on Reliable Engineering Computing
Guest Editors: Rafi L. Muhanna and Robert L. Mullen
Formulation for Reliable Analysis of Structural
Frames
George Corliss, Christopher Foley, and
R. Baker Kearfott 125 - 147
Linear Systems with Large Uncertainties,
with Applications to Truss Structures
Arnold Neumaier and Andrzej Pownuk 149 - 172
Interval Finite Elements as a Basis for
Generalized Models of Uncertainty in
Engineering Mechanics
Rafi L. Muhanna, Hao Zhang, and Robert L. Mullen 173 - 194
A Search Algorithm for Calculating Validated
Reliability Bounds
Fulvio Tonon 195 - 209
Solving Interval Constraints by Linearization in
Computer-Aided Design
Yan Wang and Bartholomew O. Nnaji 211 - 244
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Reliable Computing. - 2007. - Vol. 13, No. 3.
Mathematical Research
On Interval Systems [x]=[A][x]+[b] and the
Powers of Interval Matrices in Complex
Interval Arithmetics
Hans-Robert Arndt 245 - 259
Unimodality, Independence Lead to NP-Hardness
of Interval Probability Problems
Daniel J. Berleant, Olga Kosheleva,
Vladik Kreinovich, and Hung T. Nguyen 261 - 282
Exponential Stability of Interval Dynamical
Systems with Quadratic Nonlinearity
Ruslan S. Ivlev and Svetlana P. Sokolova 283 - 291
Bounds on Generalized Linear Predictors with
Incomplete Outcome Data
Joerg Stoye 293 - 302
Historical Notes
Early Automatic Differentiation:
The Ch'in-Horner Algorithm
Louis B. Rall 303 - 308
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Reliable Computing. - 2007. - Vol. 13, No. 4.
Mathematical Research
A New Robust Algorithm to Trace Curves
Dominique Faudot and Dominique Michelucci 309 - 324
Extension of the Hansen-Bliek Method to
Right-Quantified Linear Systems
Gilles Chabert and Alexandre Goldsztejn 325 - 349
Guaranteed Parameter Set Estimation for
Exponential Sums: The Three-Terms Case
Juergen Garloff, Ismail Idriss, and
Andrew P. Smith 351 - 359
Solution Set Characterization of Linear
Interval Systems with a Specific Dependence
Structure
Milan Hladik 361 - 374
Information
Interval-Related Talks at the International
Conference on Finite Element Methods in
Engineering and Science
Vladik Kreinovich and Rafi Muhanna 375 - 379
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Reliable Computing. - 2007. - Vol. 13, No. 5.
Mathematical Research
Guaranteeing the Homotopy Type of a Set Defined
by Non-Linear Inequalities
Nicolas Delanoue, Luc Jaulin,
and Bertrand Cottenceau 381 - 398
Optimal Multiplication of G-intervals
Lubomir V. Kolev 399 - 408
On Sufficient Conditions of the Injectivity:
Development of a Numerical Test Algorithm
via Interval Analysis
Sebastien Lagrange, Nicolas Delanoue,
and Luc Jaulin 409 - 421
Application
An Application of Interval Methods to
Stock Market Forecasting
Chenyi Hu and Ling T. He 423 - 434
Information
Interval-Related Talks at the 2007 IEEE
Symposium Series on Computational Intelligence 435 - 440
Interval-Related Talks at the North American
Fuzzy Information Processing Society Annual
Conference NAFIPS'07 441 - 443
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Reliable Computing. - 2007. - Vol. 13, No. 6.
Mathematical Research
Determining the Positive Definiteness Margin
of Interval Matrices
Lubomir V. Kolev 445 - 466
Computing Population Variance and Entropy under
Interval Uncertainty: Linear-Time Algorithms
Gang Xiang, Martine Ceberio, and Vladik Kreinovich 467 - 488
Computing the Pessimism of Inclusion Functions
Gilles Chabert and Luc Jaulin 489 - 504
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