Convergence estimates for product iterative methods with applications to domain decomposition

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

doi:10.1090/S0025-5718-1991-1090464-8

Convergence estimates for product iterative methods with applications to domain decomposition

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

Research output: Contribution to journal › Article › peer-review

160 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. © 1991 American Mathematical Society.

Original language	English (US)
Pages (from-to)	1-21
Number of pages	21
Journal	Mathematics of Computation
Volume	57
Issue number	195
DOIs	https://doi.org/10.1090/S0025-5718-1991-1090464-8
State	Published - Jan 1 1991
Externally published	Yes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-1991-1090464-8

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AU - Pascjak, Joseph E.

AU - Wang, Junping

AU - Xu, Jinchao

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PY - 1991/1/1

Y1 - 1991/1/1

N2 - 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. © 1991 American Mathematical Society.

AB - 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. © 1991 American Mathematical Society.

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DO - 10.1090/S0025-5718-1991-1090464-8

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VL - 57

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EP - 21

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 195

ER -

Convergence estimates for product iterative methods with applications to domain decomposition

Abstract

Bibliographical note

ASJC Scopus subject areas

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