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

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.

Folkmar Bornemann is Professor and Chair of Numerical Analysis and Scientific Computing at the Center of Mathematical Sciences, Munich University of Technology, Germany. His field of research is numerical PDEs with applications to physics and chemistry. He is co-author of the textbook Scientific Computing with Ordinary Differential Equations (Springer-Verlag, 2002) and editor of the Mitteilungen der Deutschen Mathematiker-Vereinigung (Notices of the German Mathematical Society).

Dirk Laurie is Professor in the department of mathematics at the University of Stellenbosch, South Africa. His interests include most of modern numerical mathematics, with a strong emphasis on the actual implementation of algorithms. He has been involved in mathematical competitions for over twenty years as a setter of problems for the South African Mathematical Olympiad.

Stan Wagon is Professor of mathematics and computer science at Macalester College in St. Paul, Minnesota. He is an expert in the use of Mathematica, which he has used in research and teaching for many years. He is the author of ten books and eighty papers and has won numerous writing awards, including the Ford Award, the Chauvenet Prize, and the Evans Award, all awarded by the Mathematics Association of America.

Jörg Waldvogel is Professor emeritus at the Seminar for Applied Mathematics of the Swiss Federal Institute of Technology (ETH) in Zurich, Switzerland. His main fields of research are engineering mathematics, numerical analysis, celestial mechanics, complex analysis, number theory, and asymptotics. In 1976 he was awarded a prize by the Belgian Royal Academy for his contribution to the theory of the three-body problem. Since his retirement in 2003 he has remained active as a part-time teacher, committee member, counselor, and researcher.