Factored approximate inverse preconditioners with dynamic sparsity patterns

Eun Joo Lee; Jun Zhang

doi:10.1016/j.camwa.2011.04.071

Factored approximate inverse preconditioners with dynamic sparsity patterns

Eun Joo Lee, Jun Zhang

Computer Science

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

2 Scopus citations

Abstract

We propose two sparsity pattern selection algorithms for factored approximate inverse preconditioners to solve general sparse matrices. The sparsity pattern is adaptively updated in the construction phase by using combined information of the inverse and original triangular factors of the original matrix. In order to determine the sparsity pattern, our first algorithm uses the norm of the inverse factors multiplied by the largest absolute value of the original factors, and the second employs the norm of the inverse factors divided by the norm of the original factors. Experimental results show that these algorithms improve the robustness of the preconditioners to solve general sparse matrices.

Original language	English
Pages (from-to)	235-242
Number of pages	8
Journal	Computers and Mathematics with Applications
Volume	62
Issue number	1
DOIs	https://doi.org/10.1016/j.camwa.2011.04.071
State	Published - Jul 2011

Bibliographical note

Funding Information:
The first author’s research work was supported in part by the Keystone Innovation Starter Kit Grant Project under grant contract number C000032549 . The second’s research work was supported in part by the US National Science Foundation under grant CCF-0527967 , in part by the National Institutes of Health under grant 1R01HL086644-01 , in part by the Kentucky Science and Engineering Foundation under grant KSEF-148-502-06-186 , and in part by the Alzheimer’s Association under Grant NIGR-06-25460 .

Funding

The first author’s research work was supported in part by the Keystone Innovation Starter Kit Grant Project under grant contract number C000032549 . The second’s research work was supported in part by the US National Science Foundation under grant CCF-0527967 , in part by the National Institutes of Health under grant 1R01HL086644-01 , in part by the Kentucky Science and Engineering Foundation under grant KSEF-148-502-06-186 , and in part by the Alzheimer’s Association under Grant NIGR-06-25460 .

Funders	Funder number
Alzheimer’s Association	NIGR-06-25460
Keystone Innovation Starter Kit Grant Project	C000032549
US National Science Foundation	CCF-0527967
National Institutes of Health (NIH)	1R01HL086644-01
Kentucky Science and Engineering Foundation	KSEF-148-502-06-186

Keywords

Approximate inverse
Preconditioner
Sparsity pattern

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2011.04.071

Cite this

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title = "Factored approximate inverse preconditioners with dynamic sparsity patterns",

abstract = "We propose two sparsity pattern selection algorithms for factored approximate inverse preconditioners to solve general sparse matrices. The sparsity pattern is adaptively updated in the construction phase by using combined information of the inverse and original triangular factors of the original matrix. In order to determine the sparsity pattern, our first algorithm uses the norm of the inverse factors multiplied by the largest absolute value of the original factors, and the second employs the norm of the inverse factors divided by the norm of the original factors. Experimental results show that these algorithms improve the robustness of the preconditioners to solve general sparse matrices.",

keywords = "Approximate inverse, Preconditioner, Sparsity pattern",

author = "Lee, {Eun Joo} and Jun Zhang",

note = "Funding Information: The first author{\textquoteright}s research work was supported in part by the Keystone Innovation Starter Kit Grant Project under grant contract number C000032549 . The second{\textquoteright}s research work was supported in part by the US National Science Foundation under grant CCF-0527967 , in part by the National Institutes of Health under grant 1R01HL086644-01 , in part by the Kentucky Science and Engineering Foundation under grant KSEF-148-502-06-186 , and in part by the Alzheimer{\textquoteright}s Association under Grant NIGR-06-25460 . ",

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N2 - We propose two sparsity pattern selection algorithms for factored approximate inverse preconditioners to solve general sparse matrices. The sparsity pattern is adaptively updated in the construction phase by using combined information of the inverse and original triangular factors of the original matrix. In order to determine the sparsity pattern, our first algorithm uses the norm of the inverse factors multiplied by the largest absolute value of the original factors, and the second employs the norm of the inverse factors divided by the norm of the original factors. Experimental results show that these algorithms improve the robustness of the preconditioners to solve general sparse matrices.

AB - We propose two sparsity pattern selection algorithms for factored approximate inverse preconditioners to solve general sparse matrices. The sparsity pattern is adaptively updated in the construction phase by using combined information of the inverse and original triangular factors of the original matrix. In order to determine the sparsity pattern, our first algorithm uses the norm of the inverse factors multiplied by the largest absolute value of the original factors, and the second employs the norm of the inverse factors divided by the norm of the original factors. Experimental results show that these algorithms improve the robustness of the preconditioners to solve general sparse matrices.

KW - Approximate inverse

KW - Preconditioner

KW - Sparsity pattern

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Factored approximate inverse preconditioners with dynamic sparsity patterns

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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