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.
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
CountryAustria
CityKlagenfurt
Period8/09/1313/09/13

Fingerprint

GMRES
Ill-posed Problem
Dependent
Semiconvergence
Non-normality
Smallest Eigenvalue
Singular Systems
Largest Eigenvalue
Eigenvalue
Decrease
Coefficient

Keywords

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

Cite this

Pestana, J. (2014). Right-hand side dependent bounds for GMRES applied to ill-posed problems. In C. Pötzsche, C. Heuberger, B. Kaltenbacher, & F. Rendl (Eds.), System Modeling and Optimization: 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers (pp. 230-236). (IFIP Advances in Information and Communication Technology; Vol. 443). Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-662-45504-3_22
Pestana, Jennifer. / Right-hand side dependent bounds for GMRES applied to ill-posed problems. System Modeling and Optimization: 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers. editor / Christian Pötzsche ; Clemens Heuberger ; Barbara Kaltenbacher ; Franz Rendl. Heidelberg : Springer-Verlag, 2014. pp. 230-236 (IFIP Advances in Information and Communication Technology).
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Pestana, J 2014, Right-hand side dependent bounds for GMRES applied to ill-posed problems. in C Pötzsche, C Heuberger, B Kaltenbacher & F Rendl (eds), System Modeling and Optimization: 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers. IFIP Advances in Information and Communication Technology, vol. 443, Springer-Verlag, Heidelberg, pp. 230-236, 26th IFIP TC 7 Conference on System Modeling and Optimization, Klagenfurt, Austria, 8/09/13. https://doi.org/10.1007/978-3-662-45504-3_22

Right-hand side dependent bounds for GMRES applied to ill-posed problems. / Pestana, Jennifer.

System Modeling and Optimization: 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers. ed. / Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. Heidelberg : Springer-Verlag, 2014. p. 230-236 (IFIP Advances in Information and Communication Technology; Vol. 443).

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

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Pestana J. Right-hand side dependent bounds for GMRES applied to ill-posed problems. In Pötzsche C, Heuberger C, Kaltenbacher B, Rendl F, editors, System Modeling and Optimization: 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers. Heidelberg: Springer-Verlag. 2014. p. 230-236. (IFIP Advances in Information and Communication Technology). https://doi.org/10.1007/978-3-662-45504-3_22