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
Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel, The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing. SIAM, Philadelphia (2004)
Jonathan M. Borwein and David H. Bailey, Mathematics by Experiment: Plausible Reasoning in the 21st Century. AK Peters, Natick (2003)
W. Timothy Gowers, June Barrow-Green, and Imre Leader (editors), The Princeton Companion to Mathematics. Princeton University Press, Princeton (2008)
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)
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/
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© 2011 Springer-Verlag Berlin Heidelberg
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Trefethen, L.N. (2011). Ten Digit Problems. In: Schleicher, D., Lackmann, M. (eds) An Invitation to Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19533-4_9
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DOI: https://doi.org/10.1007/978-3-642-19533-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19532-7
Online ISBN: 978-3-642-19533-4
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