A new framework for multi-parameter regularization

Silvia Gazzola, Lothar Reichel

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This paper proposes a new approach for choosing the regularization parameters in multi-parameter regularization methods when applied to approximate the solution of linear discrete ill-posed problems. We consider both direct methods, such as Tikhonov regularization with two or more regularization terms, and iterative methods based on the projection of a Tikhonov-regularized problem onto Krylov subspaces of increasing dimension. The latter methods regularize by choosing appropriate regularization terms and the dimension of the Krylov subspace. Our investigation focuses on selecting a proper set of regularization parameters that satisfies the discrepancy principle and maximizes a suitable quantity, whose size reflects the quality of the computed approximate solution. Theoretical results are shown and illustrated by numerical experiments.

Original languageEnglish
Pages (from-to)919-949
Number of pages31
JournalBIT Numerical Mathematics
Volume56
Issue number3
Early online date16 Dec 2015
DOIs
Publication statusPublished - 1 Sep 2016

Keywords

  • Arnoldi–Tikhonov method
  • Discrepancy principle
  • Ill-posed problems
  • Multi-parameter Tikhonov method

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