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The SIAM 100-Digit Challenge

The SIAM 100-Digit Challenge
A Study in High-Accuracy Numerical Computing

$80.00 (P)

  • Date Published: January 1987
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898715613

$ 80.00 (P)
Paperback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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About the Authors
  • The authors, members of teams that solved all 10 problems, show in detail multiple approaches for solving each problem, ranging from elementary to sophisticated, from brute-force to schemes that can be scaled to provide thousands of digits of accuracy and that can solve even larger related problems. The authors touch on virtually every major technique of modern numerical analysis: matrix computation, iterative linear methods, limit extrapolation and convergence acceleration, numerical quadrature, contour integration, discretization of PDEs, global optimization, Monte Carlo and evolutionary algorithms, error control, interval and high-precision arithmetic, and many more. The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing gives concrete examples of how to justify the validity of every single digit of a numerical answer. Methods range from carefully designed computer experiments to a posteriori error estimates and computer-assisted proofs based on interval arithmetic.

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    Product details

    • Date Published: January 1987
    • format: Paperback
    • isbn: 9780898715613
    • length: 318 pages
    • dimensions: 253 x 174 x 16 mm
    • weight: 0.564kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Foreword
    Preface
    The Story
    1. A Twisted Tail
    2. Reliability amid Chaos
    3. How Far Away Is Infinity?
    4. Think Globally
    Act Locally
    5. A Complex Optimization
    6. Biasing for a Fair Return
    7. Too Large to Be Easy
    Too Small to Be Hard
    8. In the Moment of Heat
    9. Gradus ad Parnassum
    10. Hitting the Ends
    Appendix A. Convergence Acceleration
    Appendix B. Extreme Digit-Hunting
    Appendix C. Code
    Appendix D. More Problems
    References
    Index.

  • Authors

    Folkmar Bornemann, Universität Munchen

    Dirk Laurie, University of Stellenbosch, South Africa

    Stan Wagon, Macalester College, Minnesota

    Jörg Waldvogel, Swiss Federal Institute of Technology, Zürich

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