Wavelet sparse approximate inverse preconditioners

Tony Chan*, W. P. Tang, W. L. Wan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 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 languageEnglish (US)
Pages (from-to)644-660
Number of pages17
JournalBIT Numerical Mathematics
Volume37
Issue number3
DOIs
StatePublished - Jan 1 1997

Keywords

  • Approximate inverses
  • Preconditioning
  • Sparse matrices
  • Wavelet

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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