David H Bailey Boeken

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 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 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 collection features 25 papers published since the 1970s, focusing on pi and related areas in mathematics and computer science. It opens with a Foreword by Bruce Berndt, and each paper includes a brief summary and a keyword list that connects it to other contributions. The articles cover various topics, including actual computations of pi, mathematical inquiries such as the normality of pi, and innovative techniques for calculating its digits, like the “BBP” algorithm, which allows for the computation of arbitrary binary digits without prior digits. The volume also presents significant mathematical results related to pi and advanced graphical methods for analyzing its properties. It serves as a companion to a previous source book on pi, with its collection starting with two foundational papers from 1976 by Eugene Salamin and Richard Brent. These papers introduced “quadratically convergent” algorithms for pi and other functions, marking the onset of modern computational mathematics. This era coincides with the rise of high-performance computing, which has seen exponential growth in power. The book appeals to a diverse audience, offering advanced research insights for specialists while remaining accessible to undergraduate students in mathematics.