Inheritance of the discrete Picard condition in Krylov subspace methods

Silvia Gazzola, Paolo Novati

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

When projection methods are employed to regularize linear discrete ill-posed problems, one implicitly assumes that the discrete Picard condition (DPC) is somehow inherited by the projected problems. In this paper we show that, under some assumptions, the DPC holds for the projected uncorrupted systems computed by various Krylov subspace methods. By exploiting the inheritance of the DPC, some estimates on the behavior of the projected problems are also derived. Numerical examples are provided in order to illustrate the accuracy of the derived estimates.

Original languageEnglish
Pages (from-to)893-918
JournalBIT Numerical Mathematics
Volume56
Issue number3
DOIs
Publication statusPublished - Sep 2016

Keywords

  • Arnoldi algorithm
  • Discrete Picard condition
  • GMRES residual
  • Iterative regularization
  • Lanczos bidiagonalization algorithm

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