C++ Toolbox for Verified Computing I

Basic Numerical Problems Theory, Algorithms, and Programs

  • Ulrich Kulisch
  • Rolf Hammer
  • Matthias Hocks
  • Dietmar Ratz

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Introduction

    1. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 1-14
  3. Preliminaries

    1. Front Matter
      Pages 15-15
    2. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 17-29
    3. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 30-53
  4. One-Dimensional Problems

    1. Front Matter
      Pages 55-55
    2. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 57-69
    3. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 70-92
    4. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 93-112
    5. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 113-139
    6. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 140-163
    7. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 164-185
  5. Multi-Dimensional Problems

    1. Front Matter
      Pages 187-187
    2. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 189-209
    3. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 210-243
    4. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 244-292
    5. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 293-311
    6. Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 312-342
  6. Back Matter
    Pages 343-382

About this book

Introduction

This C++ Toolbox for Verified Computing presents an extensive set of sophisticated tools for solving basic numerical problems with verification of the results. It is the C++ edition of the Numerical Toolbox for Verified Computing which was based on the computer language PASCAL-XSC. The sources of the programs in this book are freely available via anonymous ftp. This book offers a general discussion on arithmetic and computational reliablility, analytical mathematics and verification techniques, algoriths, and (most importantly) actual C++ implementations. In each chapter, examples, exercises, and numerical results demonstrate the application of the routines presented. The book introduces many computational verification techniques. It is not assumed that the reader has any prior formal knowledge of numerical verification or any familiarity with interval analysis. The necessary concepts are introduced. Some of the subjects that the book covers in detail are not usually found in standard numerical analysis texts.

Keywords

C++ und C-XSC Intervallarithmetik Numerik Selbstverifizierende Numerik algorithm algorithms automatic result automatische Ergebnisverifikation c++ and c-xsc interval arithmetic self-validating numerics simplification of programming verificatio

Authors and affiliations

  • Ulrich Kulisch
    • 1
  • Rolf Hammer
    • 1
  • Matthias Hocks
    • 1
  • Dietmar Ratz
    • 1
  1. 1.Institut für Angewandte MathematikUniversität KarlsruheKarlsruheGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-79651-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-79653-1
  • Online ISBN 978-3-642-79651-7
  • About this book