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Perspectives on Enclosure Methods

  • Book
  • © 2001

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Editors:
  1. Ulrich Kulisch

    1. Universität Karlsruhe, Institut für Angewandte Mathematik

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  2. Rudolf Lohner

    1. Universität Karlsruhe, Institut für Angewandte Mathematik

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  3. Axel Facius

    1. Universität Karlsruhe, Institut für Angewandte Mathematik

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  • Introduction to a most advanced research field in scientific computing

  • Interesting applications

  • Latest research results

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-XII
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  2. Proving Conjectures by Use of Interval Arithmetic

    • Andreas Frommer
    Pages 1-12

  3. Advanced Arithmetic for the Digital Computer — Interval Arithmetic Revisited

    • Ulrich W. Kulisch
    Pages 15-70

  4. Highly Accurate Verified Error Bounds for Krylov Type Linear System Solvers

    • Axel Facius
    Pages 77-97

  5. Elements of Scientific Computing

    • J. Hartmut Bleher
    Pages 99-103

  6. The Mainstreaming of Interval Arithmetic

    • John L. Gustafson
    Pages 105-117

  7. Bounds for Eigenvalues with the Use of Finite Elements

    • Henning Behnke, Ulrich Mertins
    Pages 119-131

  8. Algorithmic Differencing

    • Louis B. Rall, Thomas W. Reps
    Pages 133-146

  9. A Comparison of Techniques for Evaluating Centered Forms

    • Bruno Lang
    Pages 149-155

  10. On the Limit of the Total Step Method in Interval Analysis

    • Günter Mayer, Ingo Warnke
    Pages 157-171

  11. How Fast can Moore’s Interval Integration Method Really be?

    • Jürgen Herzberger
    Pages 173-179

  12. Numerical Verification and Validation of Kinematics and Dynamical Models for Flexible Robots in Complex Environments

    • Wolfram Luther, Eva Dyllong, Daniela Fausten, Werner Otten, Holger Traczinski
    Pages 181-198

  13. On the Ubiquity of the Wrapping Effect in the Computation of Error Bounds

    • Rudolf J. Lohner
    Pages 201-216

  14. A New Perspective on the Wrapping Effect in Interval Methods for Initial Value Problems for Ordinary Differential Equations

    • Nedialko S. Nedialkov, Kenneth R. Jackson
    Pages 219-263

  15. A Guaranteed Bound of the Optimal Constant in the Error Estimates for Linear Triangular Elements

    • Mitsuhiro T. Nakao, Nobito Yamamoto
    Pages 265-275

  16. Nonsmooth Global Optimization

    • Dietmar Ratz
    Pages 277-337

  17. Back Matter

    Pages 341-345
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Keywords

About this book

Enclosure methods and their applications have been developed to a high standard during the last decades. These methods guarantee the validity of the computed results. This means they are of the same standard as the rest of mathematics. The book deals with a wide variety of aspects of enclosure methods. All contributions follow the common goal to push the limits of enclosure methods forward. Topics that are treated include basic questions of arithmetic, proving conjectures, bounds for Krylow type linear system solvers, bounds for eigenvalues, the wrapping effect, algorithmic differencing, differential equations, finite element methods, application in robotics, and nonsmooth global optimization.

Editors and Affiliations

  • Universität Karlsruhe, Institut für Angewandte Mathematik

    Ulrich Kulisch, Rudolf Lohner, Axel Facius

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