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Stabilized approximate inverse preconditioners for indefinite matrices

Published: 28 March 2008 Publication History

Abstract

A two-phase preconditioning strategy based on a factored sparse approximate inverse is proposed for solving sparse indefinite matrices. In each phase, the strategy first makes the original matrix diagonally dominant to enhance the stability by a shifting method, and constructs an inverse approximation of the shifted matrix by utilizing a factored sparse approximate inverse preconditioner. The two inverse approximation matrices produced from each phase are then combined to be used as a preconditioner. Experimental results show that the presented strategy improves the accuracy and the stability of the preconditioner on solving indefinite sparse matrices. Furthermore, the strategy ensures that convergence rate of the preconditioned iterations of the two-phase preconditioning strategy is much better than that of the standard sparse approximate inverse ones for solving indefinite matrices.

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cover image ACM Other conferences
ACMSE '08: Proceedings of the 46th annual ACM Southeast Conference
March 2008
548 pages
ISBN:9781605581057
DOI:10.1145/1593105
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 28 March 2008

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  1. factored approximate inverse preconditioner
  2. indefinite matrices

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ACM SE08
ACM SE08: ACM Southeast Regional Conference
March 28 - 29, 2008
Alabama, Auburn

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