The SIAM 100-Digit Challenge

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.

Spis treści:
Foreword
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
Appendix A. Convergence Acceleration
Appendix B. Extreme Digit-Hunting
Appendix C. Code
Appendix D. More Problems
References
Index.