Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems

Jennifer Pestana

Research output: Chapter in Book/Report/Conference proceedingChapter


© IFIP International Federation for Information Processing 2014. 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 (US)
Title of host publicationIFIP Advances in Information and Communication Technology
PublisherSpringer Nature
Number of pages7
ISBN (Print)9783662455036
StatePublished - Nov 28 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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