Right-hand side dependent bounds for GMRES applied to ill-posed problems

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Abstract

In this paper we apply simple GMRES bounds to the nearly singular systems that arise in ill-posed problems. Our bounds depend on the eigenvalues of the coefficient matrix, the right-hand side vector and the nonnormality of the system. The bounds show that GMRES residuals initially decrease, as residual components associated with large eigenvalues are reduced, after which semi-convergence can be expected because of the effects of small eigenvalues.
Original languageEnglish
Title of host publicationSystem Modeling and Optimization
Subtitle of host publication26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers
EditorsChristian Pötzsche, Clemens Heuberger, Barbara Kaltenbacher, Franz Rendl
Place of PublicationHeidelberg
PublisherSpringer-Verlag
Pages230-236
Number of pages7
ISBN (Print)9783662455036
DOIs
Publication statusPublished - 28 Nov 2014
Event26th IFIP TC 7 Conference on System Modeling and Optimization - Klagenfurt, Austria
Duration: 8 Sep 201313 Sep 2013

Publication series

NameIFIP Advances in Information and Communication Technology
PublisherSpringer-Verlag
Volume443
ISSN (Print)1868-4238

Conference

Conference26th IFIP TC 7 Conference on System Modeling and Optimization
Country/TerritoryAustria
CityKlagenfurt
Period8/09/1313/09/13

Keywords

  • GMRES
  • convergence
  • ill-posed problem
  • eigenvalues
  • generalized minimal residual method

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