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Extrapolation methods in numerical integration

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Abstract

Extrapolation methods have been used for many years for numerical integration. The most well-known of these methods is Romberg integration. A survey by Joyce on the use of extrapolation in numerical analysis appeared in 1971 in which a substantial portion is devoted to numerical integration. In this paper, we shall survey progress made in this field since 1971. The topics surveyed include partition-extrapolation methods for dealing with singular integrands, the work of Lyness and others in generating asymptotic expansions for the error functional in one and several dimensions, the work of de Doncker and others on adaptive extrapolation and the work of Sidi and others on the evaluation of highly oscillatory infinite integrals by extrapolation. Other extrapolation techniques will be mentioned briefly.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Philip Rabinowitz

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  1. Philip Rabinowitz
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Rabinowitz, P. Extrapolation methods in numerical integration. Numer Algor 3, 17–28 (1992). https://doi.org/10.1007/BF02141912

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