Abstract

Most quantitative mathematical problems cannot be solved exactly, but there are powerful algorithms for solving many of them numerically to a specified degree of precision like ten digits or ten thousand. In this article three difficult problems of this kind are presented, and the story is told of the SIAM 100-Dollar, 100-Digit Challenge. The twists and turns along the way illustrate some of the flavor of algorithmic continuous mathematics.

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Further Reading

  1. [1]
    Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel, The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing. SIAM, Philadelphia (2004) MATHGoogle Scholar
  2. [2]
    Jonathan M. Borwein and David H. Bailey, Mathematics by Experiment: Plausible Reasoning in the 21st Century. AK Peters, Natick (2003) Google Scholar
  3. [3]
    W. Timothy Gowers, June Barrow-Green, and Imre Leader (editors), The Princeton Companion to Mathematics. Princeton University Press, Princeton (2008) MATHGoogle Scholar
  4. [4]
    T. Wynn Tee and Lloyd N. Trefethen, A rational spectral collocation method with adaptively transformed Chebyshev grid points. SIAM Journal of Scientific Computing 28, 1798–1811 (2006) MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Lloyd N. Trefethen, Ten digit algorithms. Numerical Analysis Technical Report NA-05/13, Oxford University Computing Laboratory. http://www.comlab.ox.ac.uk/oucl/publications/natr/

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Oxford University Mathematical InstituteOxfordUK

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