Error Estimation in Ill-Posed Problems in Special Cases

Anatoly G. Yagola, Yury M. Korolev

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

1 Citation (SciVal)

Abstract

In this review we consider ill-posed inverse problems for linear operator equations Az = u with an operator A acting between two normed spaces. It is well known that, in general, no error estimate can be provided for approximate solution of an ill-posed problem. But in some special cases when we are aware of some a priori information about the unknown exact solution, error estimation can be done. In this paper we review inverse problems on compact sets, as well as inverse problems with source-wise represented solutions. We also touch inverse problems in partially ordered spaces. A posteriori error estimates for regularized solutions with special regularization properties are also discussed here. This work was supported by the Swedish institute (Visby program) and the RFBR grants 11-01-0040_a and 12-01-00524_a.

Original languageEnglish
Title of host publicationApplied Inverse Problems - Select Contributions from the First Annual Workshop on Inverse Problems
EditorsL. Beilina
Place of PublicationNew York, U. S. A.
PublisherSpringer New York
Pages155-164
Number of pages10
ISBN (Print)9781461478157
DOIs
Publication statusPublished - 1 Jan 2013
Event1st Annual Workshop on Inverse Problems - Gothenburg, Sweden
Duration: 2 Jun 20113 Jun 2011

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume48
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference1st Annual Workshop on Inverse Problems
Country/TerritorySweden
CityGothenburg
Period2/06/113/06/11

Keywords

  • A posteriori error estimation
  • Ill-posed problems
  • Regularizing algorithms

ASJC Scopus subject areas

  • General Mathematics

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