Automatic parameter setting for Arnoldi-Tikhonov methods

Silvia Gazzola, Paolo Novati

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

In the framework of iterative regularization techniques for large-scale linear ill-posed problems, this paper introduces a novel algorithm for the choice of the regularization parameter when performing the Arnoldi-Tikhonov method. Assuming that we can apply the discrepancy principle, this new strategy can work without restrictions on the choice of the regularization matrix. Moreover, this method is also employed as a procedure to detect the noise level whenever it is just overestimated. Numerical experiments arising from the discretization of integral equations and image restoration are presented.

Original languageEnglish
Pages (from-to)180-195
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume256
Early online date6 Aug 2013
DOIs
Publication statusPublished - 15 Jan 2014

Keywords

  • Arnoldi algorithm
  • Discrepancy principle
  • Image restoration
  • Tikhonov regularization

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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