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The SIAM 100-Digit Challenge: A contest in high-accuracy numerical computing
In Feb. 2002 Nick 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 teams achieved perfect scores of 100 digits. I will discuss the solutions to several of the problems.
One of the harder ones was: Which cubic polynomial is the best approximation to &ob;\it 1/Gamma(z)&cb; in the unit disk, using the sup-norm?
One of the easier ones was: What is the minimum value of the function
sin(60e^y) + sin(70 sin x) + sin(sin[80 y]) - sin[10(x+y)] + (1/4)(x^2+y^2) + e^(sin(50x))?
Subsidiary challenges were (1) the computation of the ten answers to 10000 digits, and (2) the proof of correctness of digits. I and three others (F. Bornemann, D. Laurie, and J. Waldvogel) wrote a book about the contest and we have been successful in obtaining 10000 digits for nine of the ten problems and in using interval arithmetic to prove the correctness of the results in seven of the ten cases.
Host: Alexandr Kostochka and Doug West
Thursday, November 4, 2004, 245 Altgeld Hall, 4 p.m.
Mathematics Colloquia homepage