Shadow block iteration for solving linear systems obtained from wavelet transforms

Yao Lu, Lixin Shen, Yuesheng Xu

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

Matrices resulting from wavelet transforms have a special "shadow" block structure, that is, their small upper left blocks contain their lower frequency information. Numerical solutions of linear systems with such matrices require special care. We propose shadow block iterative methods for solving linear systems of this type. Convergence analysis for these algorithms are presented. We apply the algorithms to three applications: linear systems arising in the classical regularization with a single parameter for the signal de-blurring problem, multilevel regularization with multiple parameters for the same problem and the Galerkin method of solving differential equations. We also demonstrate the efficiency of these algorithms by numerical examples in these applications.

Original languageEnglish (US)
Pages (from-to)359-385
Number of pages27
JournalApplied and Computational Harmonic Analysis
Volume19
Issue number3
DOIs
StatePublished - Nov 1 2005
Externally publishedYes

Keywords

  • Block iterations
  • Deblurring
  • Regularization
  • Wavelets

ASJC Scopus subject areas

  • Applied Mathematics

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