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Article type: Research Article
Authors: Levin, Davida | Sidi, Avramb
Affiliations: [a] School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel. E-mail: levin@math.tau.ac.il | [b] Computer Science Department, Technion - Israel Institute of Technology, Haifa 32000, Israel. E-mail: asidi@cs.technion.ac.il
Abstract: Methods for the numerical evaluation of multi-dimensional infinite-range integrals and infinite series are reviewed. Particular emphasis is put on those methods that are based on the generalized Richardson extrapolation (GREP) of Sidi and the Levin-Sidi D- and d-transformations for one-dimensional integrals and series respectively. After summarizing in detail the essentials of the D- and d-transformations, the paper first discusses an approach due to Sidi that makes sequential use of the D- and d-transformations in multidimensional problems. Next a multi-dimensional version of GREP is introduced and recent generalizations of the D- and d-transformations that are due to Greif and Levin are discussed. All these are based on a careful analysis of the asymptotic expansions of suitably defined remainders.
Keywords: Convergence acceleration, multiple series, multi-dimensional integrals, multivariate extrapolation
Keywords: 40A05, 40A10, 40A25, 40A30, 40B05, 41A60, 41A63, 65B05, 65B10
DOI: 10.3233/JCM-2001-12-303
Journal: Journal of Computational Methods in Sciences and Engineering, vol. 1, no. 2-3, pp. 167-184, 2001
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