On Krylov projection methods and Tikhonov regularization

Silvia Gazzola, Paolo Novati, Maria Rosaria Russo

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)

Abstract

In the framework of large-scale linear discrete ill-posed problems, Krylov projection methods represent an essential tool since their development, which dates back to the early 1950's. In recent years, the use of these methods in a hybrid fashion or to solve Tikhonov regularized problems has received great attention especially for problems involving the restoration of digital images. In this paper we review the fundamental Krylov-Tikhonov techniques based on Lanczos bidiagonalization and the Arnoldi algorithms. Moreover, we study the use of the unsymmetric Lanczos process that, to the best of our knowledge, has just marginally been considered in this setting. Many numerical experiments and comparisons of different methods are presented.

Original languageEnglish
Pages (from-to)83-123
Number of pages41
JournalElectronic Transactions on Numerical Analysis
Volume44
Publication statusPublished - 2015

Keywords

  • Arnoldi algorithm
  • Discrepancy principle
  • Discrete ill-posed problems
  • Generalized cross validation
  • Image deblurring
  • Krylov projection methods
  • L-curve criterion
  • Lanczos bidiagonalization
  • Nonsymmetric lanczos process
  • Regińska criterion
  • Tikhonov regularization

ASJC Scopus subject areas

  • Numerical Analysis

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