Wavelet sparse approximate inverse preconditioners

T. F. Chan; W. P. Tang; W. L. Wan

doi:10.1007/BF02510244

Wavelet sparse approximate inverse preconditioners

T. F. Chan^*, W. P. Tang, W. L. Wan

^*Corresponding author for this work

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

49 Scopus citations

Abstract

We show how to use wavelet compression ideas to improve the performance of approximate inverse preconditioners. Our main idea is to first transform the inverse of the coefficient matrix into a wavelet basis, before applying standard approximate inverse techniques. In this process, smoothness in the entries of A^-1 are converted into small wavelet coefficients, thus allowing a more efficient approximate inverse approximation. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverses.

Original language	English (US)
Pages (from-to)	644-660
Number of pages	17
Journal	BIT Numerical Mathematics
Volume	37
Issue number	3
DOIs	https://doi.org/10.1007/BF02510244
State	Published - Sep 1997
Externally published	Yes

Keywords

Approximate inverses
Preconditioning
Sparse matrices
Wavelet

ASJC Scopus subject areas

Software
Computer Networks and Communications
Computational Mathematics
Applied Mathematics

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10.1007/BF02510244

Cite this

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title = "Wavelet sparse approximate inverse preconditioners",

abstract = "We show how to use wavelet compression ideas to improve the performance of approximate inverse preconditioners. Our main idea is to first transform the inverse of the coefficient matrix into a wavelet basis, before applying standard approximate inverse techniques. In this process, smoothness in the entries of A-1 are converted into small wavelet coefficients, thus allowing a more efficient approximate inverse approximation. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverses.",

keywords = "Approximate inverses, Preconditioning, Sparse matrices, Wavelet",

author = "Chan, {T. F.} and Tang, {W. P.} and Wan, {W. L.}",

note = "Funding Information: SThe work was supported by the Natural Sciences and Engineering Research Council of Canada, the Information Technology Research Centre (which is funded by the Province of Ontario), and RIACS/NASA Ames NAS 2-96027. Funding Information: *Received September 1996. Revised January 1997. tSupported by grants from ONR: ONR-N00014-92-J-1890, and the Army Research Office: DAAL-03-91-C-0047 (Univ. of Tenn. subcontract ORA4466.04 Amendment 1 and 2). The first and the third author also acknowledge support from RIACS/NASA Ames NAS 2-96027 and the Alfred P. Sloan Foundation as Doctoral Dissertation Fellows, respectively.",

year = "1997",

month = sep,

doi = "10.1007/BF02510244",

language = "English (US)",

volume = "37",

pages = "644--660",

journal = "BIT Numerical Mathematics",

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AU - Chan, T. F.

AU - Tang, W. P.

AU - Wan, W. L.

N1 - Funding Information: SThe work was supported by the Natural Sciences and Engineering Research Council of Canada, the Information Technology Research Centre (which is funded by the Province of Ontario), and RIACS/NASA Ames NAS 2-96027. Funding Information: *Received September 1996. Revised January 1997. tSupported by grants from ONR: ONR-N00014-92-J-1890, and the Army Research Office: DAAL-03-91-C-0047 (Univ. of Tenn. subcontract ORA4466.04 Amendment 1 and 2). The first and the third author also acknowledge support from RIACS/NASA Ames NAS 2-96027 and the Alfred P. Sloan Foundation as Doctoral Dissertation Fellows, respectively.

PY - 1997/9

Y1 - 1997/9

N2 - We show how to use wavelet compression ideas to improve the performance of approximate inverse preconditioners. Our main idea is to first transform the inverse of the coefficient matrix into a wavelet basis, before applying standard approximate inverse techniques. In this process, smoothness in the entries of A-1 are converted into small wavelet coefficients, thus allowing a more efficient approximate inverse approximation. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverses.

AB - We show how to use wavelet compression ideas to improve the performance of approximate inverse preconditioners. Our main idea is to first transform the inverse of the coefficient matrix into a wavelet basis, before applying standard approximate inverse techniques. In this process, smoothness in the entries of A-1 are converted into small wavelet coefficients, thus allowing a more efficient approximate inverse approximation. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverses.

KW - Approximate inverses

KW - Preconditioning

KW - Sparse matrices

KW - Wavelet

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JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

IS - 3

ER -

Wavelet sparse approximate inverse preconditioners

Abstract

Keywords

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