Numerical Validation in Current Hardware Architectures

1. Front Matter

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2. Standardization/Hardware

   1. Discussions on an Interval Arithmetic Standard at Dagstuhl Seminar 08021

      • R. Baker Kearfott, John Pryce, Nathalie Revol

      Pages 1-6

   2. Complete Interval Arithmetic and Its Implementation on the Computer

      • Ulrich W. Kulisch

      Pages 7-26

3. Tools

   1. Continued Fractions for Special Functions: Handbook and Software

      • Annie Cuyt, Franky Backeljauw, Stefan Becuwe, Michel Colman, Tom Docx, Joris Van Deun

      Pages 27-40

   2. A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range

      • Frithjof Blomquist, Werner Hofschuster, Walter Krämer

      Pages 41-67

   3. C-XSC and Closely Related Software Packages

      • Werner Hofschuster, Walter Krämer, Markus Neher

      Pages 68-102

   4. Extending the Range of C-XSC: Some Tools and Applications for the Use in Parallel and Other Environments

      • Markus Grimmer

      Pages 103-116

   5. Mathematica Connectivity to Interval Libraries filib++ and C-XSC

      • Evgenija D. Popova

      Pages 117-132

4. Applications

   1. Some Applications of Interval Arithmetic in Hierarchical Solid Modeling

      • Eva Dyllong

      Pages 133-144

   2. Numerical Verification Assessment in Computational Biomechanics

      • Ekaterina Auer, Wolfram Luther

      Pages 145-160

   3. Robustness of Boolean Operations on Subdivision-Surface Models

      • Di Jiang, Neil F. Stewart

      Pages 161-174

   4. Towards the Development of an Interval Arithmetic Environment for Validated Computer-Aided Design and Verification of Systems in Control Engineering

      • Andreas Rauh, Johanna Minisini, Eberhard P. Hofer

      Pages 175-188

   5. Distributed Bounded-Error Parameter and State Estimation in Networks of Sensors

      • Michel Kieffer

      Pages 189-202

   6. Error Bounds for Lanczos Approximations of Rational Functions of Matrices

      • Andreas Frommer, Valeria Simoncini

      Pages 203-216

5. Linear Systems

   1. Error-Free Transformation in Rounding Mode toward Zero

      • Stef Graillat, Jean-Luc Lamotte, Diep Nguyen Hong

      Pages 217-229

   2. Fast (Parallel) Dense Linear System Solvers in C-XSC Using Error Free Transformations and BLAS

      • Walter Krämer, Michael Zimmer

      Pages 230-249

   3. A Note on Solving Problem 7 of the SIAM 100-Digit Challenge Using C-XSC

      • Mariana Kolberg, Walter Krämer, Michael Zimmer

      Pages 250-261

6. Back Matter

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This book constitutes the thoroughly refereed post-proceedings of the Dagstuhl Seminar 08021 on Numerical Validation in Current Hardware Architectures held at Dagstuhl Castle, Germany, in January 2008. The 16 revised full papers presented were selected during two rounds of reviewing and improvements. The papers are organized in topical sections on languages, software systems and tools, new verification techniques based on interval arithmetic, applications in science and engineering, and novel approaches to verification.

• C-XSC
• CAD
• IEEE 754
• IEEE 854
• biomechanics
• continued fractions
• filib
• floating point
• interval arithmetic
• mathematica
• multiple precision arithmetic
• sensor networks
• solid modeling
• subdivision surfaces
• verification

• Department of Mathematics and Computer Science, Universiteit Antwerpen, Antwerpen, Belgium

  Annie Cuyt

• Wissenschaftliches Rechnen/Softwaretechnologie, Bergische Universität Wuppertal, Wuppertal, Germany

  Walter Krämer

• Fakultät Ingenieurwissenschaften, Abteilung Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, Duisburg, Germany

  Wolfram Luther

• Woodside, USA

  Peter Markstein

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