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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- Jonathan M. Borwein and David H. Bailey, Mathematics by Experiment: Plausible Reasoning in the 21st Century. AK Peters, Natick (2003) Google Scholar
- 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/