The SIAM 100-digit challenge. Study in high-accuracy numerical computing

Folkmar Bornemann, Dirk Laurie, Stan Wagon, Jörg Waldvogel9780898715613, 089871561X

This book takes readers on a thrilling tour of some of the most important and powerful areas of contemporary numerical mathematics. The tour is organized along the 10 problems of the SIAM 100-Digit Challenge, a contest posed by Nick Trefethen of Oxford University in the January/February 2002 issue of SIAM News. The complete story of the contest as well as a lively interview with Nick Trefethen are also included.
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.
This book will aid readers in developing problem-solving skills for making judicious method selections. The chapters may be read independently. Appendices A and B include basic methods of convergence acceleration and details of computing the solutions to very high accuracy. Full code for all the methods, examples, tables, and figures is given (partly in Appendix C, completely on the accompanying web page).The code is written in a variety of languages, including Mathematica, Matlab, Maple, C, Octave, and PARI/GP. Appendix D offers a sample of additional challenging problems for those who master some of the techniques discussed here.

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Table of contents :
Foreword……Page 3
Preface……Page 5
The Story……Page 11
A Twisted Tail……Page 27
Reliability amid Chaos……Page 43
How Far Away Is Infinity?……Page 57
Think Globally, Act Locally……Page 87
A Complex Optimization……Page 113
Biasing for a Fair Return……Page 133
Too Large to Be Easy, Too Small to Be Hard……Page 159
In the Moment of Heat……Page 181
Gradus ad Parnassum……Page 193
Hitting the Ends……Page 211
Convergence Acceleration……Page 237
Extreme Digit-Hunting……Page 273
Code……Page 277
More Problems……Page 297
Index……Page 303