The SIAM 100-Digit Challenge: a decade later. Inspirations, ramifications, and other eddies left in its wake. (English) Zbl 1341.65001
Summary: In 2002, L.N. Trefethen of Oxford University challenged the scientific community by ten intriguing mathematical problems to be solved, numerically, to ten digit accuracy each (I was one of the successful contestants; in 2004, jointly with three others of them, I published a book [F. Bornemann et al., The SIAM 100-digit challenge. A study in high-accuracy numerical computing. With a foreword by David H. Bailey. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2004; Zbl 1060.65002)] on the manifold ways of solving those problems). In this paper, I collect some new and noteworthy insights and developments that have evolved around those problems in the last decade or so. In the course of my tales, I will touch mathematical topics as diverse as divergent series, Ramanujan summation, low-rank approximations of functions, hybrid numeric-symbolic computation, singular moduli, self-avoiding random walks, the Riemann prime counting function, and winding numbers of planar Brownian motion. As was already the intention of the book, I hope to encourage the reader to take a broad view of mathematics, since one lasting moral of Trefethen’s contest is that overspecialization will provide too narrow a view for one with a serious interest in computation.
MSC:
| 65-03 | History of numerical analysis |
| 40A05 | Convergence and divergence of series and sequences |
| 40D05 | General theorems on summability |
| 41A29 | Approximation with constraints |
| 68W30 | Symbolic computation and algebraic computation |
| 60G50 | Sums of independent random variables; random walks |
| 11A41 | Primes |
| 60J65 | Brownian motion |
Keywords:
divergent series; numeric-symbolic methods; low-rank approximation; singular moduli; self-avoiding random walk; Riemann \(R\) function; Ramanujan summation; random walk; winding number; Brownian motionCitations:
Zbl 1060.65002References:
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