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C++ Toolbox for Verified Computing I

Basic Numerical Problems Theory, Algorithms, and Programs

  • Book
  • © 1995

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Authors:
  1. Ulrich Kulisch

    1. Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

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  2. Rolf Hammer

    1. Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

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  3. Matthias Hocks

    1. Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

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  4. Dietmar Ratz

    1. Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Introduction

    1. Introduction

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 1-14

  3. Preliminaries

    1. Front Matter

      Pages 15-15
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    2. The Features of C-XSC

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 17-29

    3. Mathematical Preliminaries

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 30-53

  4. One-Dimensional Problems

    1. Front Matter

      Pages 55-55
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    2. Evaluation of Polynomials

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 57-69

    3. Automatic Differentiation

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 70-92

    4. Nonlinear Equations in One Variable

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 93-112

    5. Global Optimization

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 113-139

    6. Evaluation of Arithmetic Expressions

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 140-163

    7. Zeros of Complex Polynomials

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 164-185

  5. Multi-Dimensional Problems

    1. Front Matter

      Pages 187-187
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    2. Linear Systems of Equations

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 189-209

    3. Linear Optimization

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 210-243

    4. Automatic Differentiation for Gradients, Jacobians, and Hessians

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 244-292

    5. Nonlinear Systems of Equations

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 293-311

    6. Global Optimization

      • Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz
      Pages 312-342

  6. Back Matter

    Pages 343-382
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Keywords

About this book

Our aim in writing this book was to provide an extensive set of C++ programs for solving basic numerical problems with verification of the results. This C++ Toolbox for Verified Computing I is the C++ edition of the Numerical Toolbox for Verified Computing l. The programs of the original edition were written in PASCAL-XSC, a PASCAL eXtension for Scientific Computation. Since we published the first edition we have received many requests from readers and users of our tools for a version in C++. We take the view that C++ is growing in importance in the field of numeri­ cal computing. C++ includes C, but as a typed language and due to its modern concepts, it is superior to C. To obtain the degree of efficiency that PASCAL-XSC provides, we used the C-XSC library. C-XSC is a C++ class library for eXtended Scientific Computing. C++ and the C-XSC library are an adequate alternative to special XSC-Ianguages such as PASCAL-XSC or ACRITH-XSC. A shareware version of the C-XSC library and the sources of the toolbox programs are freely available via anonymous ftp or can be ordered against reimbursement of expenses. The programs of this book do not require a great deal of insight into the features of C++. Particularly, object oriented programming techniques are not required.

Authors and Affiliations

  • Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

    Ulrich Kulisch, Rolf Hammer, Matthias Hocks, Dietmar Ratz

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