By Folkmar Bornemann, Dirk Laurie, Stan Wagon, Jörg Waldvogel

ISBN-10: 089871561X

ISBN-13: 9780898715613

This can be a solid booklet containing much approximately excessive accuracy computation. Ten difficulties are mentioned with info concerning many components of arithmetic. loads of codes of many arithmetic software program are proven with a precious appendix. an internet web page of this publication can also be a spotlight. you may as well perform with it exhaustingly and enjoyably.

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New PDF release: The SIAM 100-Digit Challenge: A Study in High-Accuracy

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Extra info for The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing

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5d is adequate when working to d digits. This page intentionally left blank Chapter 2 Reliability amid Chaos Stan Wagon If I venture to displace ... the microscopical speck of dust... upon the point of my finger, ... I have done a deed which shakes the Moon in her path, which causes the Sun to be no longer the Sun, and which alters forever the destiny of multitudinous myriads of stars.... —Edgar Allen Poe (Eureka, 1848) But every jet of chaos which threatens to exterminate us is convertible by intellect into wholesome force.

This allows us to take advantage of a nifty trick for repeatedly integrating by parts. v)) = x for all x in the region of interest. 7. Representation as a Divergent Series 25 and in general In this case, taking c = /, f(y) = W(y), g(x) = xex , all derivatives o f / vanish at infinity. 5). For 16 digits, it is adequate to consider only the range 0 ^ t ^ 12. Romberg integration is still adequate, but this integrand is not so easy, and 131,073 function evaluations are needed to confirm the result from the previous method.

9. Going for 10,000 Digits 31 Infinite Series. We cannot use this method as our main tool, but if its result happens to agree with our other well-founded methods, it is useful as a confidence booster. Contour integration on the infinite interval typically requires step size inversely proportional to the number of digits. 9) as a function of t (once from the parametrization, once from the exponentiation in the integrand) guarantees that the number of points required increases only slightly faster than the inverse of the step size, so that the number of points N actually used is modelled by yy = O(d{+e), where € is small.

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The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing by Folkmar Bornemann, Dirk Laurie, Stan Wagon, Jörg Waldvogel


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