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

Folkmar Bornemann
Organization: Munich University of Technology
Department: Center of Mathematical Sciences
Dirk Laurie
Stan Wagon
Organization: Macalester College
Department: Department of Mathematics and Computer Science
URL: http://www.stanwagon.com/
Jörg Waldvogel
Book information

Publisher: Society for Industrial and Applied Mathematics (Philadelphia)
Copyright year: 2004
ISBN: 089871561X
Medium: Paperback
Pages: 306
Out of print?: N
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Book cover image

Foreword | Preface | The Story | A Twisted Tail | Reliability amid Chaos | How Far Away Is Infinity? | Think Globally, Act Locally | A Complex Optimization | Biasing for a Fair Return | Too Large to Be Easy, Too Small to Be Hard | In the Moment of Heat | Gradus ad Parnassum | Hitting the Ends | Convergence Acceleration | Extreme Digit-Hunting | Code | More Problems | References | Index

The SIAM 100-Digit Challenge was a contest posed by Nick Trefethen of Oxford University in the January/February 2002 issue of SIAM News. This book shows in detail how each of those problems can be solved, as described by four authors who belonged to winning teams that successfully solved all 10 problems. The book presents multiple approaches to the solution for each problem, including schemes that can be scaled to provide thousand-digit accuracy if required and can solve even larger related problems. In the process, the authors visit just about every major technique of modern numerical analysis: matrix computation, numerical quadrature, limit extrapolation, error control, interval arithmetic, contour integration, iterative linear methods, global optimization, high-precision arithmetic, evolutionary algorithms, eigenvalue methods, and many more. Code is provided for many Mathematica solutions, including some from the perfect-score entry submitted by the Wolfram Research team.

*Mathematics > Algebra > Linear Algebra
*Mathematics > Calculus and Analysis
*Mathematics > Calculus and Analysis > Complex Analysis
*Mathematics > Calculus and Analysis > Dynamical Systems
*Mathematics > Calculus and Analysis > Special Functions
*Mathematics > Probability and Statistics
*Mathematics > Recreational Mathematics

large-scale linear algebra, computational complex analysis, special functions and the arithmetic-geometric mean, Fourier analysis, asymptotic expansions, convergence acceleration, discretizations that converge exceptionally fast, symbolic computing, global optimization