Numerical Software with Result Verification

International Dagstuhl Seminar, Dagstuhl Castle, Germany, January 19-24, 2003. Revised Papers

  • René Alt
  • Andreas Frommer
  • R. Baker Kearfott
  • Wolfram Luther
Conference proceedings

DOI: 10.1007/b96498

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2991)

Table of contents (18 papers)

  1. Front Matter
  2. Languages

    1. 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
  4. New Verification Techniques Based on Interval Arithmetic

    1. 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
    2. Interval Algorithms in Modeling of Multibody Systems
      Ekaterina Auer, Andrés Kecskeméthy, Martin Tändl, Holger Traczinski
      Pages 132-159
    3. Reliable Distance and Intersection Computation Using Finite Precision Geometry
      Katja Bühler, Eva Dyllong, Wolfram Luther
      Pages 160-190
    4. 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. Result Verification for Computational Problems in Geodesy
      Stefan Borovac, Gerhard Heindl
      Pages 226-242
    3. Global Optimization in the COCONUT Project
      Hermann Schichl
      Pages 243-249
    4. An Application of Wavelet Theory to Early Breast Cancer
      Baya Oussena, Abderrezak Henni, René Alt
      Pages 250-258
  6. Novel Approaches to Verification

    1. Novel Approaches to Numerical Software with Result Verification
      Laurent Granvilliers, Vladik Kreinovich, Norbert Müller
      Pages 274-305
    2. Static Analysis-Based Validation of Floating-Point Computations
      Sylvie Putot, Eric Goubault, Matthieu Martel
      Pages 306-313
  7. Back Matter

About these proceedings

Introduction

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.

Keywords

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

Editors and affiliations

  • René Alt
    • 1
  • Andreas Frommer
    • 2
  • R. Baker Kearfott
    • 3
  • Wolfram Luther
    • 4
  1. 1.CNRS, UMR 7606, LIP6University Pierre et Marie CurieParis cedex 05France
  2. 2.Fachbereich C, Mathematik und NaturwissenschaftenBergische Universität WuppertalWuppertalGermany
  3. 3.University of Louisiana at Lafayette 
  4. 4.Universität Duisburg-EssenDuisburgGermany

Bibliographic information

  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-21260-7
  • Online ISBN 978-3-540-24738-8
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349