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Convergence Estimates for Product Iterative Methods with Applications to Domain Decomposition

James H. Bramble, Joseph E. Pasciak, Junping Wang and Jinchao Xu
Mathematics of Computation
Vol. 57, No. 195 (Jul., 1991), pp. 1-21
DOI: 10.2307/2938660
Stable URL: http://www.jstor.org/stable/2938660
Page Count: 21
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Convergence Estimates for Product Iterative Methods with Applications to Domain Decomposition
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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 norm-reduction 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.

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