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Quasi-random integration in high dimensions

✍ Scribed by George Takhtamyshev; Bart Vandewoestyne; Ronald Cools

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 696 KB
Volume: 73
Category: Article
ISSN: 0378-4754
DOI: 10.1016/j.matcom.2006.04.001

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we show that the Sobol' and Richtmyer sequences can be effectively used for numerical integration of functions having up to 1000 variables. The results of integration obtained with the two sequences are compared and the parameters C and α from the convergence model C/N α are estimated, where N is the number of points used. For all the tests done, the Sobol' sequence demonstrated somewhat better convergence, but for many practical values of N the relative error is higher than for Richtmyer sequences due to the large value of C. Constructing Sobol' sequences also takes considerably more time than constructing Richtmyer sequences.

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