Iterative methods by SPD and small subspace solvers for nonsymmetric or idefinite problems

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Abstract

This paper is devoted to a class of iterative methods for solving nonsymmetric or indefinite problems that are dominated by some SPD (symmetric positive definite) problems. The algorithm is based on a direct solver for the original equation restricted on a small subspace and a given iterative method for the SPD equation. It is shown that any convergent iterative method for the SPD problem will give rise to an algorithm that converges with a comparable rate if the small subspace is properly chosen. Furthermore a number of preconditioners that can be used with GMRES type methods are also obtained.

Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods for Partial Differential Equations
PublisherPubl by Soc for Industrial & Applied Mathematics Publ
Pages106-118
Number of pages13
ISBN (Print)0898712882
StatePublished - Dec 1 1992
EventFifth International Symposium on Domain Decomposition Methods for Partial Differential Equations - Norfolk, VA, USA
Duration: May 6 1991May 8 1991

Publication series

NameDomain Decomposition Methods for Partial Differential Equations

Other

OtherFifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
CityNorfolk, VA, USA
Period5/6/915/8/91

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All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

Xu, J. (1992). Iterative methods by SPD and small subspace solvers for nonsymmetric or idefinite problems. In Domain Decomposition Methods for Partial Differential Equations (pp. 106-118). (Domain Decomposition Methods for Partial Differential Equations). Publ by Soc for Industrial & Applied Mathematics Publ.