Convergence estimates for product iterative methods with applications to domain decomposition

Jamesh Bramble, Joseph E. Pascjak, Junping Wang, Jinchao Xu

Research output: Contribution to journalArticlepeer-review

151 Scopus citations

Abstract

In this paper, we consider iterative methods for the solution of symmetric positive definite problems on a space "V which are defined in terms of products of operators defined with respect to a number of subspaces. The simplest algorithm of this sort has an error-reducing operator which is the product of orthogonal projections onto the complement of the subspaces. New normreduction estimates for these iterative techniques will be presented in an abstract setting. Applications are given for overlapping Schwarz algorithms with many subregions for finite element approximation of second-order elliptic problems.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalMathematics of Computation
Volume57
Issue number195
DOIs
StatePublished - Jul 1991

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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