On two variants of an algebraic wavelet preconditioner

Tony F. Chan*, Ke Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

A recursive method of constructing preconditioning matrices for the nonsymmetric stiffness matrix in a wavelet basis is proposed for solving a class of integral and differential equations. It is based on a level-by-level application of the wavelet scales decoupling the different wavelet levels in a matrix form just as in the well-known nonstandard form. The result is a powerful iterative method with built-in preconditioning leading to two specific algebraic multilevel iteration algorithms: one with an exact Schur preconditioning and the other with an approximate Schur preconditioning. Numerical examples are presented to illustrate the efficiency of the new algorithms.

Original languageEnglish (US)
Pages (from-to)260-283
Number of pages24
JournalSIAM Journal on Scientific Computing
Volume24
Issue number1
DOIs
StatePublished - Apr 15 2003
Externally publishedYes

Keywords

  • Level-by-level transforms
  • Multilevel preconditioner
  • Multiresolution
  • Schur complements
  • Sparse approximate inverse
  • Wavelets

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'On two variants of an algebraic wavelet preconditioner'. Together they form a unique fingerprint.

Cite this