A NEW APPROACH TO COMPUTE SPARSE APPROXIMATE INVERSE OF AN SPD MATRIX

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KHOJASTEH SALKUYEH D.; TOUTOUNIAN F.

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Paper Information

Journal: INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE (ENGLISH) Year:2004 | Volume:15 | Issue:4 Page(s): 87-95

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Title

A NEW APPROACH TO COMPUTE SPARSE APPROXIMATE INVERSE OF AN SPD MATRIX

Author(s)

KHOJASTEH SALKUYEH D. | TOUTOUNIAN F. | Issue Writer Certificate

Keywords

SPARSE APPROXIMATE INVERSE

SYMMETRIC POSITIVE DEFINITE MATRIX

PRECONDITIONING

KRYLOV SUBSPACE METHODS

Abstract

In this paper, a new algorithm to solve a symmetric positive definite linear system of equations is proposed. Then, by exploiting the algorithm a new approach to compute a SPARSE APPROXIMATE INVERSE M of a SYMMETRIC POSITIVE DEFINITE MATRIX A is presented. The new approach is based on minimizing the Frobenius norm of the residual matrix AM - I and can be decoupled into n subproblems, where n is the dimension of A and I is identity matrix. Hence the computation of the preconditioner can be done in parallel. In this approach the sparsity of the approximate inverse is preserved only by specifying the number of the nonzero elements of each column of M in advance. Some numerical experiments on test matrices from Harwell-Boeing collection are presented to make a comparison with the similar available methods.

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APA: Copy

KHOJASTEH SALKUYEH, D., & TOUTOUNIAN, F.. (2004). A NEW APPROACH TO COMPUTE SPARSE APPROXIMATE INVERSE OF AN SPD MATRIX. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE (ENGLISH), 15(4), 87-95. SID. https://sid.ir/paper/529454/en

Vancouver: Copy

KHOJASTEH SALKUYEH D., TOUTOUNIAN F.. A NEW APPROACH TO COMPUTE SPARSE APPROXIMATE INVERSE OF AN SPD MATRIX. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE (ENGLISH)[Internet]. 2004;15(4):87-95. Available from: https://sid.ir/paper/529454/en

IEEE: Copy

D. KHOJASTEH SALKUYEH, and F. TOUTOUNIAN, “A NEW APPROACH TO COMPUTE SPARSE APPROXIMATE INVERSE OF AN SPD MATRIX,” INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE (ENGLISH), vol. 15, no. 4, pp. 87–95, 2004, [Online]. Available: https://sid.ir/paper/529454/en

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