Extrapolation Methods for Infinite Multiple Series and Integrals

David Levin, Avram Sidi

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)167-184
Number of pages18
JournalJournal of Computational Methods in Sciences and Engineering
Volume1
Issue number2-3
DOIs
StatePublished - 2001

Keywords

  • Convergence acceleration
  • multi-dimenional integrals
  • multi-vibrate extrapolation
  • multiple series

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