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

  Folkmar Bornemann · Dirk Laurie · Stan Wagon · Jörg Waldvogel

       
 

   SIAM, 2004, xii+306pp, ISBN 0-89871-561-X
 

The following links point to a lot of further material. Most important, we adhere to the significant concept of reproducible computational science by including all the source code for the numerical experiments, figures, and tables that are presented in the book.

Contents

Foreword by David H. Bailey
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
A    Convergence Acceleration
B    Extreme Digit Hunting
C    Code
D    More Problems
References
Index

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Destined to be a classic of modern computational science―a gourmet feast in ten courses.
―from the foreword by David H. Bailey, Lawrence Berkeley National Laboratory.

From the back cover

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 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. Full code for all the methods, examples, tables, and figures is given on the accompanying web page, www.siam.org/books/100digitchallenge.

Folkmar Bornemann is Professor of Numerical Analysis and Scientific Computing at the Center of Mathematical Sciences, Technische Universität München, Germany.

Dirk Laurie is Professor of Mathematics at the University of Stellenbosch, South Africa.

Stan Wagon is Professor of Mathematics and Computer Science at Macalester College, St. Paul, Minnesota, USA.
 
Jörg Waldvogel is Professor Emeritus at the Seminar for Applied Mathematics of the Swiss Federal Institute of Technology (ETH) Zurich, Zurich, Switzerland.

last modified: 10/25/05 14:15 +0200 (FB)