Embedded techniques for choosing the parameter in Tikhonov regularization

S. Gazzola, P. Novati, M. R. Russo

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy principle, although no initial knowledge of the norm of the error that affects the right-hand side is assumed; an increasingly more accurate approximation of this quantity is recovered during the Arnoldi algorithm. Some theoretical estimates are derived in order to motivate our approach. Many numerical experiments performed on classical test problems as well as image deblurring problems are presented.

Original languageEnglish
Pages (from-to)796-812
Number of pages17
JournalNumerical Linear Algebra with Applications
Volume21
Issue number6
Early online date3 Apr 2014
DOIs
Publication statusPublished - 1 Dec 2014

Keywords

  • Arnoldi algorithm
  • Discrepancy principle
  • Linear discrete ill-posed problems
  • Tikhonov regularization

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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