








The SIAM 100Digit Challenge: A Study in HighAccuracy Numerical Computing






Organization:  Munich University of Technology 
Department:  Center of Mathematical Sciences 
Organization:  Macalester College 
Department:  Department of Mathematics and Computer Science 






Publisher:  Society for Industrial and Applied Mathematics (Philadelphia) 
  






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 DigitHunting  Code  More Problems  References  Index






The SIAM 100Digit 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 thousanddigit 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, highprecision arithmetic, evolutionary algorithms, eigenvalue methods, and many more. Code is provided for many Mathematica solutions, including some from the perfectscore entry submitted by the Wolfram Research team.












largescale linear algebra, computational complex analysis, special functions and the arithmeticgeometric mean, Fourier analysis, asymptotic expansions, convergence acceleration, discretizations that converge exceptionally fast, symbolic computing, global optimization







   
 
