Numerical Software with Result Verification

1. Front Matter

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2. Languages

   1. OOP and Interval Arithmetic – Language Support and Libraries

      • Jürgen Wolff von Gudenberg

      Pages 1-14

   2. C-XSC 2.0 – A C++ Library for Extended Scientific Computing

      • Werner Hofschuster, Walter Krämer

      Pages 15-35

3. Software Systems and Tools

   1. Libraries, Tools, and Interactive Systems for Verified Computations Four Case Studies

      • R. Baker Kearfott, Markus Neher, Shin’ichi Oishi, Fabien Rico

      Pages 36-63

   2. Multiple Precision Interval Packages: Comparing Different Approaches

      • Markus Grimmer, Knut Petras, Nathalie Revol

      Pages 64-90

   3. Interval Testing Strategies Applied to COSY’s Interval and Taylor Model Arithmetic

      • George F. Corliss, Jun Yu

      Pages 91-106

4. New Verification Techniques Based on Interval Arithmetic

   1. Nonlinear Parameter and State Estimation for Cooperative Systems in a Bounded-Error Context

      • Michel Kieffer, Eric Walter

      Pages 107-123

   2. Guaranteed Numerical Computation as an Alternative to Computer Algebra for Testing Models for Identifiability

      • Eric Walter, Isabelle Braems, Luc Jaulin, Michel Kieffer

      Pages 124-131

   3. Interval Algorithms in Modeling of Multibody Systems

      • Ekaterina Auer, Andrés Kecskeméthy, Martin Tändl, Holger Traczinski

      Pages 132-159

   4. Reliable Distance and Intersection Computation Using Finite Precision Geometry

      • Katja Bühler, Eva Dyllong, Wolfram Luther

      Pages 160-190

   5. On Singular Interval Systems

      • Götz Alefeld, Günter Mayer

      Pages 191-197

5. Applications in Science and Engineering

   1. Result-Verifying Solution of Nonlinear Systems in the Analysis of Chemical Processes

      • Thomas Beelitz, Christian Bischof, Bruno Lang, Klaus Schulte Althoff

      Pages 198-205

   2. Verified Numerical Analysis of the Performance of Switching Systems in Telecommunication

      • Daniela Fausten, Gerhard Haßlinger

      Pages 206-225

   3. Result Verification for Computational Problems in Geodesy

      • Stefan Borovac, Gerhard Heindl

      Pages 226-242

   4. Global Optimization in the COCONUT Project

      • Hermann Schichl

      Pages 243-249

   5. An Application of Wavelet Theory to Early Breast Cancer

      • Baya Oussena, Abderrezak Henni, René Alt

      Pages 250-258

6. Novel Approaches to Verification

   1. Using PVS to Validate the Inverse Trigonometric Functions of an Exact Arithmetic

      • David Lester

      Pages 259-273

   2. Novel Approaches to Numerical Software with Result Verification

      • Laurent Granvilliers, Vladik Kreinovich, Norbert Müller

      Pages 274-305

   3. Static Analysis-Based Validation of Floating-Point Computations

      • Sylvie Putot, Eric Goubault, Matthieu Martel

      Pages 306-313

7. Back Matter

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Reliable computing techniques are essential if the validity of the output of a - merical algorithm is to be guaranteed to be correct. Our society relies more and more on computer systems. Usually, our systems appear to work successfully, but there are sometimes serious, and often minor, errors. Validated computing is one essential technology to achieve increased software reliability. Formal - gor in the de?nition of data types, the computer arithmetic, in algorithm design, and in program execution allows us to guarantee that the stated problem has (or does not have) a solution in an enclosing interval we compute. If the enclosure is narrow, we are certain that the result can be used. Otherwise, we have a clear warning that the uncertainty of input values might be large and the algorithm and the model have to be improved. The use of interval data types and al- rithms with controlled rounding and result veri?cation capture uncertainty in modeling and problem formulation, in model parameter estimation, in algorithm truncation, in operation round-o?, and in model interpretation. The techniques of validated computing have proven their merits in many scienti?c and engineering applications. They are based on solid and interesting theoretical studies in mathematics and computer science. Contributions from ?elds including real, complex and functional analysis, semigroups, probability, statistics,fuzzyintervalanalysis,fuzzylogic,automaticdi?erentiation,computer hardware, operating systems, compiler construction, programming languages, object-oriented modeling, parallel processing, and software engineering are all essential.

• C++ programming language
• algorithms
• computer algebra
• floating-point computations
• guaranteed numerical computations
• interval arithmetic
• modeling
• numerical analysis
• object-oriented programming (OOP)
• optimization
• reliable computing
• result verification
• validated computing
• validated numerical software
• verification
• algorithm analysis and problem complexity

• CNRS, UMR 7606, LIP6, University Pierre et Marie Curie, Paris cedex 05, France

  René Alt

• Fachbereich C, Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Wuppertal, Germany

  Andreas Frommer

• University of Louisiana at Lafayette,  

  R. Baker Kearfott

• Universität Duisburg-Essen, Duisburg, Germany

  Wolfram Luther

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