Perspectives on Enclosure Methods

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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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.

• Boundary value problem
• Eigenvalue
• Factor
• algorithms
• calculus
• computation
• derivative
• differential equation
• finite element method
• mathematics
• numerical analysis
• numerics
• optimization
• ordinary differential equation
• scientific computing

• Universität Karlsruhe, Institut für Angewandte Mathematik

  Ulrich Kulisch, Rudolf Lohner, Axel Facius

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