Books on Interval Computations
Books on Interval Computations
- Interval and Fuzzy Analysis: A Unified
Approach, by Weldon Lodwick, Elsevier, 2007.
- Introduction
to Precise Numerical Methods, by Oliver Aberth, Elsevier, 2007.
- Linear
Optimization Problems with Inexact Data, by M. Fiedler, J.
Nedoma, J. Ramik, J. Rohn, and K. Zimmermann, Springer Verlag, 2006,
ISBN: 0-387-32697-9; for Table of Contents, click
here
- Russian translation
of Numerical Toolbox for Verified Computing,
by R. Hammer, M. Hocks, U. Kulisch, D. Ratz
(Springer-Verlag, New York, 1993), 2005;
edited by V. Kreinovich, A. N. Sobolevski, and A. G. Yakovlev.
- Global Optimization Using Internal
Analysis, by E. R. Hansen and G. W. Walster, MIT Press,
Cambridge, Massachusetts, 2004.
- Inclusion Methods for Nonlinear Problems
With Applications in Engineering, Economics and Physics, by
J. Herzberger (ed.), Springer-Verlag, Wien, 2003.
- Advanced Arithmetic for the Digital
Computer, by
Ulrich W. Kulisch, Springer-Verlag, Wien, 2002.
- Applied Interval Analysis, with
Examples in Parameter and State Estimation, Robust Control and
Robotics, by Luc Jaulin, Michel Kieffer, Olivier Didrit,
and Eric Walter, Springer-Verlag, London, 2001, ISBN 1-85233-219-0.
- Scientific Computing, Validated Numerics,
Interval Methods, edited by
Walter Kraemer and Juergen Wolff v. Gudenberg,
Kluwer, Boston/Dordrecht/London, 2001.
- Perspectives on Enclosure
Methods, edited by U. Kulisch, R. Lohner, and A. Facius,
Springer-Verlag, Vienna, 2001, ISBN 3-211-83590-3.
- Introduction to Numerical
Analysis by Arnold Neumaier, Cambridge Univ. Press,
Cambridge, 2001, ISBN-0-521-333237 (hardback), ISBN 0-521-336104
(paperback).
- Russian translation of R. Klatte, U. Kulisch, M. Neaga, D. Ratz, and
Ch. Ullrich, PASCAL-XSC - Language Reference with
Examples (Springer-Verlag, New York, 1992), Moscow, Terevinf,
2000; edited by V. Chiriaev and A. G. Yakovlev (click here for the Editor's Introduction).
- Developments in Reliable
Computing, edited by Tibor Csendes, Kluwer, Dordrecht,
1999.
- Precise Numerical Analysis Using
C++, by Oliver Aberth, Academic Press, 1998.
- Complex Interval Arithmetic and Its
Applications, by Miodrag S. Petkovic and Ljiljana D.
Petkovic, John Wiley, 1998, ISBN 3-527-40134-2.
- Automatic
Slope Computation and its Application in Nonsmooth
Global Optimization by Dietmar Ratz, Shaker-Verlag, Aachen, 1998,
ISBN 3-826574093-X.
- Self-Validated
Numerical Methods and Applications, by Luiz H. de Figueiredo and
Jorge Stolfi, (Brazilian Mathematics Colloquium monograph),
IMPA, Rio de Janeiro, Brazil, July 1997.
- Computational Complexity and Feasibility
of Data Processing and Interval Computations, by Vladik
Kreinovich, Anatoly Lakeyev, Jiri Rohn, and Patrick Kahl, Kluwer,
Dordrecht, 1997.
- Identification of Parametric Models from
Experimental Data, by Eric Walter and L. Pronzato
Springer-Verlag, Berlin-Heidelberg, 1997
- Scientific Computing and Validated
Numerics, edited by Goetz Alefeld, Andreas Frommer, and Bruno
Lang, Akademie-Verlag, 1996
- Rigorous
Global Search: Continuous Problems by R. Baker
Kearfott , Kluwer, Dordrecht, 1996
- Applications of Interval
Computations, edited by R. Baker Kearfott and Vladik Kreinovich,
Kluwer, 1996
- Software Engineering in Scientific
Computing, by W. Mackens and Sigfried M. Rump, Vieweg, 1996
- Bounding Approaches to System
Identification, edited by: Mario Milanese, John
Norton, Helene Piet-Lahanier, and Eric Walter, Plenum, New York,
1996
- m-M Calculus,
by Slavisa Presic, Matematicki institut, Beograd, 1996, ISBN
86-80593-19-2.
-
Topics in Validated Computations: Proceedings of
IMACS-GAMM International Workshop on Validated
Computations, Oldenburg, Germany,
by Juergen Herzberger (Editor),
Elsevier, 1994, ISBN 0444816852.
-
Numerical Toolbox for Verified Computing
Information on the book
and software; in German and English:
Pascal (1993) and
C++ (1995) versions
-
Interval Methods for Circuit Analysis,
by L. V. Kolev,
World Scientific, 1993, ISBN
9810214138.
- Global Optimization Using Interval
Analysis, by Elden R. Hansen, Marcel Dekker, New York,
1992, ISBN 0824786963.
- Interval Methods for Systems of
Equations, by Arnold Neumaier, Cambridge University Press,
Cambridge, 1990, ISBN 0-521-33196-X; the book is still available
from Cambridge University Press and from amazon.com
-
Wissenschaftliches Rechnen mit Ergebnisverifikation,
by Ulrich Kulisch (Editor), Friedr. Vieweg und
Sohn, Braunschweig/Wiesbaden, 1989.
-
Iterative Methods for Simultaneous Inclusion of
Polynomial Zeros,
by Miodrag Petkovic,
Springer Verlag, 1989, ISBN 0387514856.
- Precise Numerical Analysis, by
Oliver Aberth, Wm. C. Brown,
Dubuque, Iowa, 1988
A somewhat older numerical analysis text constructed
around the "precision arithmetic" version of interval arithmetic.
-
Reliability in Computing: The Role of Interval Methods
in Scientific Computing,
by Ramon E. Moore (Editor), Academic Press, N.Y., 1988,
ISBN 0125056303.
-
New Computer Methods for Global Optimization,
by H. Ratschek and J. Rokne,
Ellis Horwood, Chicester, 1988
The book can be downloaded as a
pdf
file
-
Interval Mathematics 1985,
by K. Nickel (Editor), Springer-Verlag, 1985.
-
Computer Methods for the Range of Functions,
by H. Ratschek and J. Rokne,
Halsted Press, 1984, ISBN 0470200340.
- Introduction to Interval
Computations,
by Goetz Alefeld and Juergen Herzberger, Academic Press, N.Y., 1983.
- Introduction to Numerical Methods of
Interval Mathematics (in Russian),
Irutsk University Publ., Irkutsk, Russia, 1982.
- Computer Arithmetic in Theory and
Practice,
by Ulrich Kulisch, Academic Press, 1981, ISBN 012428650X.
-
Interval Mathematics 1980,
by K. Nickel (Editor), Academic Press, N.Y., 1980.
-
Methods and Applications of Interval Analysis,
by Ramon E. Moore,
Society for Industrial &
Applied Mathematics, Philadelphia, 1979, ISBN
0898711614.
- Mathematical Elements of Scientific
Computing, by Ramon E. Moore,
Holt, Rinehart and Winston, Inc., 1975.
-
Interval Mathematics,
by K. Nickel (Editor), Springer-Verlag, 1975.
- Interval Analysis,
by Ramon E. Moore,
Prentice-Hall, Englewood Cliffs, NJ, 1966.
Dissertations on Interval Computations
- The Use of
Interval-Related Expert
Knowledge in Processing 2D and 3D Data, with an Emphasis on
Applications to Geosciences and Biosciences, by Roberto
Araiza, 2007.
- Steigungen
höherer Ordnung zur verifizierten globalen Optimierung, by Marco
Schnurr (in German), 2007.
- Fast
Algorithms for Computing Statistics under
Interval Uncertainty, with Applications to Computer Science and to
Electrical and Computer Engineering, by Gang Xiang, 2007.
- Definition
et Applications des Extensions des Fonctions Reelles aux Intervalles
Generalises: Nouvelle Formulation de la Theorie des Intervalles
Modaux et Nouveaux Resultats, by Alexandre Goldsztejn, 2005.
- Analysis
of cable-stayed bridges by fuzzy finite element modelling, by M.
V. Rama Rao, 2004. (also posted at Dr. Pownuk's
website)
- Application of
Modal Interval Analysis to the simulation of the behaviour of dynamic
systems with uncertain parameters, by Joaquim Armengol Llobet,
1999.
- Zur Minimierung
nichtdifferenzierbarer programmierbarer Funktionen,
by Christiane Sonnenschein (in German), 1999.
Books of Interest to Interval Researchers
- Interval/Probabilistic Uncertainty and
Non-Classical Logics, by V.-N. Huynh, Y. Nakamori, H. Ono,
J. Lawry, V. Kreinovich, and H. T. Nguyen, (Eds.), Springer Verlag,
Berlin-Heidelberg, 2008, ISBN 978-3-540-77663-5
- Algorithms and Architectures of Artificial
Intelligence, by Enn Tyugu, IOS Press, Amsterdam, 2007.
- Symbolic Data Analysis: Conceptual
Statistics and Data Mining, by L. Billard and E. Diday,
John Wiley, 2007.
- New Approaches to Circle Packing in a
Square: With Program Codes, by P. G. Szabo, M. Cs.
Markot, T. Csendes, E. Specht, L. G. Casado, and I. Garcia, Springer
Verlag, 2007, ISBN 978-0387456737
This
book uses interval computations.
- Models and
Algorithms for Global Optimization, dedicated to Antanas
Zilinskas on the occasion of his 60th birthday, edited by Aimo Torn
and Julius Zilinskas, Springer Verlag, 2007, ISBN 0-387-36720-9
- Uncertainty Modeling and Analysis in
Engineering and the Sciences, by Bilal M. Ayyub and
George J. Klir, Chapman & Hall/CRC Press, 2006, ISBN: 1-584-88644-7
Among other techniques, the book covers
interval analysis and interval-valued probabilities.
- Information-Gap Decision Theory:
Decisions Under Severe Uncertainty,
by Yakov Ben-Haim, Academic Press, 2nd edition, 2006, ISBN
0-12-373552-1
- Real
Analysis: A Constructive Approach, by Mark Bridger, Wiley, 2006,
ISBN 978-0-471-79230-7.
This book uses
interval arithmetic to construct the real numbers from the rational
numbers.
- Uncertainty and Information:
Foundations of Generalized Information Theory, by G. J.
Klir, Wiley, 2006, ISBN 0-471-74867-6.
- Computational
Functional Analysis, by Ramon E. Moore and Michael Cloud,
Horwood Publishing, 2006, ISBN 1904275-24-9.
- The Statistical Analysis of
Interval-censored Failure Time Data, by Jianguo Sun,
Springer Verlag, 2006, ISBN 0-387-32905-6.
- Accuracy
and Reliability in Scientific Computing, edited by Bo Einarsson,
SIAM, Philadelphia, 2005, ISBN 0-89871-584-9.
- Analyzing Uncertainty in Civil
Engineering, by
W. Fellin, H. Lessmann, M. Oberguggenberger, and R. Vieider (eds.),
Springer-Verlag, Berlin, 2005.
- Elementary
functions, algorithms and implementations, by Jean-Michel
Muller, Springer Verlag, 2005; see also publisher
website
- An Ontological and Epistemological
Perspective of Fuzzy Set Theory,
by I. Burhan Turksen, Elsevier, 2005, ISBN 978-0444518910
- Fuzzy Statistics,
by James J. Buckley, Springer-Verlag, 2004.
- Safety Factors and Reliability: Friends or
Foes?,
by Isaac Elishakoff, Kluwer Academic Publishers, 2004, ISBN 1-4020-1779-0
(e-book ISBN 1-4020-2131-3)
In addition to probabilistic uncertainty,
this book also deals with ellipsoidal and more general convex
descriptions of uncertainty.
- Uncertain
Input Data Problems and the Worst Scenario Method, by Ivan
Hlavacek, Jan Chleboun, and Ivo Babuska, Elsevier, Amsterdam, 2004,
ISBN 0-444-51435-X.
- Optimization
Theory, by
Hubertus Th. Jongen, Klaus Meer, and Eberhard Triesch, Kluwer Academic
Publishers, Boston, 2004, ISBN 1-4020-8098-0.
- Fuzzy Randomness: Uncertainty in Civil
Engineering and Computational Mechanics, by Bernd Moeller
and Michael Beer, Springer, New York, 2004, ISBN 978-3540402947.
- Engineering
Reliability Design Handbook, by Efstratios Nikolaidis,
Dan Ghiocel, and Suren Singhal (editors), CRC Press, 2004.
- Fuzzy Probabilities and Fuzzy Sets for
Web Planning,
by James J. Buckley, Springer-Verlag, 2003, ISBN 3-540-00473-4.
- Finite Element
Methods for Structures with Large Stochastic Variations, by
Isaac Elishakoff and Yongjian Ren, Oxford University Press, 2003.
The last chapter contains a comparison of
stochastic and interval finite element methods.
- Partial Identification of Probability
Distributions,
by Charles F. Manski,
Springer-Verlag, New York, 2003, ISBN 0-387-00454-8.
- Granular Computing: An Introduction, by
Andrej Bargiela and Witold Pedrycz,
Kluwer, 2002.
- Automatic
Differentiation of Algorithms:
From Simulation to Optimization,
edited by George Corliss, Christele Faure, Andreas Griewank,
Laurent Hascoet, and Uwe Naumann,
Springer Verlag, 2002, ISBN: 0-387-95305-1
-
Scientific Computing on Itanium-based Systems,
by Marius Cornea, Ping Tak Peter Tang, and John Harrison
Intel Press, 2002, ISBN 0971288771.
-
Computable Calculus,
by Oliver Aberth,
Academic Press, 2001, ISBN 0-120-41752-9.
- Symbolic Algebraic Methods and
Verification Methods,
by Goetz Alefeld, Jiri Rohn, Siegfried Rump, and Nobito Yamamoto (editors),
Springer-Verlag, Wien, 2001, ISBN 3211835938.
- Information-Gap Decision Theory:
Decisions Under Severe Uncertainty,
by Yakov Ben-Haim, Academic Press, 2001, ISBN 0-12-088251-5.
- Computability
and Complexity in Analysis, edited by
Jens Blanck, Vasco Brattka, and Peter Hertling,
Springer-Verlag, Berlin-Heidelberg-New York, 2001,
ISBN 3-540-42197-1.
-
Encylopedia of Optimization,
edited by Christodoulos A. Floudas and Panos M. Pardalos,
Kluwer Academic Publishers, 2001, ISBN 0-792-36932-7.
- Uncertain Rule-Based
Fuzzy Logic Systems: Introduction and New Directions,
by Jerry M. Mendel, Prentice-Hall, 2001.
-
Granular Computing: An Emerging Paradigm,
edited by Witold Pedrycz,
Springer-Verlag, 2001, ISBN 3-7908-1387-7.
- Introduction to the Theory of
Differential Inclusions,
by Georgi V. Smirnov,
American Mathematical Society, 2001, ISBN: 0821829777
- Practical Applications of Approximate
Equations in Finance and Economics, by Manuel Tarrazo,
Quorum Books, Westport, Connecticut, 2001.
-
System Reliability Under Incomplete Information, by S. V. Gurov
and L. V. Utkin, Lubavich Publ.,
St. Petersburg, Russia, 1999 (in Russian).
- Uncertainty:
Models and Measures, by H. Guenther Natke and Yakov Ben-Haim
(eds.), Akademie Verlag, Berlin, 1997.
- Numerica:
A Modeling Language for Global Optimization by
Pascal Van Hentenryck, Laurent Michel, and Yves Deville, MIT Press,
Camridge, Massachusetts, 1997.
Numerica is a
modeling language for global optimization that makes it possible to state
nonlinear problems in a form close to the statements traditionally found in
textbooks and scientific papers. The constraint-solving algorithm of
Numerica is based on a combination of traditional numerical methods such as
interval and local methods, and constraint satisfaction techniques.
- Elementary
functions: algorithms and implementation
(see
also) by
Jean-Michel Muller,
Birkhauser Boston, 1997.
- Semiorders: Properties, Representations,
Applications, by M. Pirlot and Ph. Vincke,
Kluwer, Dordrecht, 1997.
- Robust Reliability in the Mechanical
Sciences, by Y. Ben-Haim, Springer-Verlag, Berlin, 1996.
- Robust
Control: The Parametric Approach
by S. P. Bhattacharyya, Herve Chapellat,
and Lee Keel, Prentice-Hall, 1995.
Crucial in the analysis and design of control systems, this book
presents a unified approach to robust stability theory, including both
linear and nonlinear systems, and provides a self-contained and
complete account of the available results in the field of robust
control under parametric uncertainty.
Includes the extremal properties of interval systems.
- New Tools for Robustness of Linear
Systems, by B. R. Barmish,
McMillan, New York, 1994.
-
Modelling Uncertain Data,
by Hans Bandemer (Editor),
Vch Publ., 1993, ISBN 3055015789.
- Interval Statistical Models,
by V. P. Kuznetsov, Moscow, Radio i
Svyaz Publ., 1991 (in Russian).
- Computer Aided Proofs in
Analysis, by K. R. Meyer and D. S. Schmidt (eds.),
Springer-Verlag, 1991.
-
Derivates of Interval Functions,
by Brian S. Thomson,
American Mathematical Society, Providence, RI,
1991,
ISBN 0821825038.
- Statistical Reasoning with Imprecise
Probabilities,,
by P. Walley, Chapman & Hall, N.Y., 1991.
- Convex Models of Uncertainty in Applied
Mechanics,
by Y. Ben-Haim and I. Elishakoff,
Elesevier, Amsterdam, 1990.
- Optimization in Case of
Uncertainty,
by A. P. Voshchinin and G. R. Sotirov,
Tehnika, Moscow, Sofia, 1989 (in Russian).
-
Intervallarithmetische
Dependenzanalyse in der Oekonometrie, by
Max Christoph Wewel,
Hohenheimer Volkswirtschaftliche Schriften Nr.5,
Peter Lang Verlag, Frankfurt am Main, 1987,
ISSN 0721-3085, ISBN 3-8204-9925-3.
-
Sensitivity Analysis in Linear Systems,
by Assem Deif,
Springer-Verlag, Berlin, 1986.
- Structure and Interpretation of Computer
Programs,
by Harold Abelson and Gerald Jay Sussman, MIT Press, Cambridge,
Massachusetts, 1985.
This book has a section on interval arithmetic and how to implement
it in LISP.
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