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.


Exact Formula Richardson Extrapolation Perfect Score Parking Problem Brute Force Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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) zbMATHGoogle 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) zbMATHGoogle 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) MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    Lloyd N. Trefethen, Ten digit algorithms. Numerical Analysis Technical Report NA-05/13, Oxford University Computing Laboratory.

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Oxford University Mathematical InstituteOxfordUK

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