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

Jennifer Pestana

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

© 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
Pages230-236
Number of pages7
ISBN (Print)9783662455036
DOIs
StatePublished - Nov 28 2014
Externally publishedYes

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