Multidirectional subspace expansion for one-parameter and multiparameter Tikhonov regularization

I.N. Zwaan, M.E. Hochstenbach

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4 Citations (Scopus)
84 Downloads (Pure)

Abstract

Tikhonov regularization is a popular method to approximate solutions of linear discrete ill-posed problems when the observed or measured data is contaminated by noise. Multiparameter Tikhonov regularization may improve the quality of the computed approximate solutions. We propose a new iterative method for large-scale multiparameter Tikhonov regularization with general regularization operators based on a multidirectional subspace expansion. The multidirectional subspace expansion may be combined with subspace truncation to avoid excessive growth of the search space. Furthermore, we introduce a simple and effective parameter selection strategy based on the discrepancy principle and related to perturbation results.

Original languageEnglish
Pages (from-to)990–1009
Number of pages20
JournalJournal of Scientific Computing
Volume70
Issue number3
DOIs
Publication statusPublished - 1 Mar 2017

Keywords

  • Generalized Krylov
  • Linear discrete ill-posed problem
  • Multidirectional subspace expansion
  • Multiparameter Tikhonov
  • Regularization
  • Regularization parameter
  • Subspace method
  • Subspace truncation
  • Tikhonov

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