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AN APPROXIMATE MATRIX INVERSION PROCEDURE BY PARALLELIZATION OF THE SHERMAN–MORRISON FORMULA

Published online by Cambridge University Press:  09 March 2010

KENTARO MORIYA ,
LINJIE ZHANG  and
TAKASHI NODERA
KENTARO MORIYA*
Affiliation:
Head Office, Nikon System Inc., Japan (email: [email protected])
LINJIE ZHANG
Affiliation:
College of Mathematical Sciences, Ocean University of China, Japan (email: [email protected])
TAKASHI NODERA
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Keio University, Japan (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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The Sherman–Morrison formula is one scheme for computing the approximate inverse preconditioner of a large linear system of equations. However, parallelizing a preconditioning approach is not straightforward as it is necessary to include a sequential process in the matrix factorization. In this paper, we propose a formula that improves the performance of the Sherman–Morrison preconditioner by partially parallelizing the matrix factorization. This study shows that our parallel technique implemented on a PC cluster system of eight processing elements significantly reduces the computational time for the matrix factorization compared with the time taken by a single processor. Our study has also verified that the Sherman–Morrison preconditioner performs better than ILU or MR preconditioners.

Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 1 , July 2009 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Society 2010

References

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