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In February 2002, L. N. Trefethen of Oxford University, in conjunction with SIAM, sponsored a worldwide contest in which the goal was to get 10 digits of the answer to each of 10 problems in numerical computing. The contest attracted a lot of attention: there were entries from 94 teams in 25 countries, and 20 of those teams (including two Mathematica-based teams: one from WRI and one from Macalester College) achieved perfect scores of 100 digits.
Mathematica's numerical capabilities (especially NIntegrate, NMinimize, and Interval) were especially well suited to some of these problems, and in this talk I will discuss the 10 problems and the quickest way to solve them in Mathematica.
Subsidiary challenges were (1) the computation of the 10 answers to 10,000 digits and (2) the proof of correctness of digits. The three coauthors of a recent book on the contest (F. Bornemann, D. Laurie, and J. Waldvogel) and I have been successful in obtaining 10000 digits for nine of the 10 problems and in using interval arithmetic to prove the correctness of the results in seven of the 10 cases.
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