A sparse approximate inverse preconditioner for parallel preconditioning of general sparse matrices

Jun Zhang

doi:10.1016/S0096-3003(01)00069-8

A sparse approximate inverse preconditioner for parallel preconditioning of general sparse matrices

Jun Zhang

Computer Science

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

22 Scopus citations

Abstract

A factored sparse approximate inverse is computed and used as a preconditioner for solving general sparse matrices. The algorithm is derived from a matrix decomposition algorithm for inverting dense nonsymmetric matrices. Several strategies and special data structures are proposed to implement the algorithm efficiently. Sparsity patterns of the factored inverse are exploited to reduce computational cost. The preconditioner possesses greater inherent parallelism than traditional preconditioners based on incomplete LU factorizations. Numerical experiments are used to show the effectiveness and efficiency of the proposed sparse approximate inverse preconditioner.

Original language	English
Pages (from-to)	63-85
Number of pages	23
Journal	Applied Mathematics and Computation
Volume	130
Issue number	1
DOIs	https://doi.org/10.1016/S0096-3003(01)00069-8
State	Published - Jul 25 2002

Bibliographical note

Funding Information:
This research was supported by the US National Science Foundation under grants CCR-9902022, CCR-9988165, and CCR-0043861.

Keywords

Incomplete LU factorization
Krylov subspace methods
Sparse approximate inverse
Sparse matrices

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/S0096-3003(01)00069-8

Cite this

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title = "A sparse approximate inverse preconditioner for parallel preconditioning of general sparse matrices",

abstract = "A factored sparse approximate inverse is computed and used as a preconditioner for solving general sparse matrices. The algorithm is derived from a matrix decomposition algorithm for inverting dense nonsymmetric matrices. Several strategies and special data structures are proposed to implement the algorithm efficiently. Sparsity patterns of the factored inverse are exploited to reduce computational cost. The preconditioner possesses greater inherent parallelism than traditional preconditioners based on incomplete LU factorizations. Numerical experiments are used to show the effectiveness and efficiency of the proposed sparse approximate inverse preconditioner.",

keywords = "Incomplete LU factorization, Krylov subspace methods, Sparse approximate inverse, Sparse matrices",

author = "Jun Zhang",

note = "Funding Information: This research was supported by the US National Science Foundation under grants CCR-9902022, CCR-9988165, and CCR-0043861. ",

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N1 - Funding Information: This research was supported by the US National Science Foundation under grants CCR-9902022, CCR-9988165, and CCR-0043861.

PY - 2002/7/25

Y1 - 2002/7/25

N2 - A factored sparse approximate inverse is computed and used as a preconditioner for solving general sparse matrices. The algorithm is derived from a matrix decomposition algorithm for inverting dense nonsymmetric matrices. Several strategies and special data structures are proposed to implement the algorithm efficiently. Sparsity patterns of the factored inverse are exploited to reduce computational cost. The preconditioner possesses greater inherent parallelism than traditional preconditioners based on incomplete LU factorizations. Numerical experiments are used to show the effectiveness and efficiency of the proposed sparse approximate inverse preconditioner.

AB - A factored sparse approximate inverse is computed and used as a preconditioner for solving general sparse matrices. The algorithm is derived from a matrix decomposition algorithm for inverting dense nonsymmetric matrices. Several strategies and special data structures are proposed to implement the algorithm efficiently. Sparsity patterns of the factored inverse are exploited to reduce computational cost. The preconditioner possesses greater inherent parallelism than traditional preconditioners based on incomplete LU factorizations. Numerical experiments are used to show the effectiveness and efficiency of the proposed sparse approximate inverse preconditioner.

KW - Incomplete LU factorization

KW - Krylov subspace methods

KW - Sparse approximate inverse

KW - Sparse matrices

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JF - Applied Mathematics and Computation

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A sparse approximate inverse preconditioner for parallel preconditioning of general sparse matrices

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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