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

dc.contributor.authorPestana, Jennifer
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
dc.date.accessioned2016-02-28T05:52:32Z
dc.date.available2016-02-28T05:52:32Z
dc.date.issued2014-11-28
dc.date.published-online2014-11-28
dc.date.published-print2014
dc.description.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.
dc.description.sponsorshipThis publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
dc.identifier.citationPestana J (2014) Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems. System Modeling and Optimization: 230–236. Available: http://dx.doi.org/10.1007/978-3-662-45504-3_22.
dc.identifier.doi10.1007/978-3-662-45504-3_22
dc.identifier.issn1868-4238
dc.identifier.issn1868-422X
dc.identifier.journalIFIP Advances in Information and Communication Technology
dc.identifier.urihttp://hdl.handle.net/10754/599513
dc.publisherSpringer Nature
dc.subjectConvergence
dc.subjectGMRES
dc.subjectIll-posed problem
dc.titleRight-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems
dc.typeBook Chapter
display.details.left<span><h5>Type</h5>Book Chapter<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Pestana, Jennifer,equals">Pestana, Jennifer</a><br><br><h5>KAUST Grant Number</h5>KUK-C1-013-04<br><br><h5>Online Publication Date</h5>2014-11-28<br><br><h5>Print Publication Date</h5>2014<br><br><h5>Date</h5>2014-11-28</span>
display.details.right<span><h5>Abstract</h5>© 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.<br><br><h5>Citation</h5>Pestana J (2014) Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems. System Modeling and Optimization: 230–236. Available: http://dx.doi.org/10.1007/978-3-662-45504-3_22.<br><br><h5>Acknowledgements</h5>This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Springer Nature,equals">Springer Nature</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=IFIP Advances in Information and Communication Technology,equals">IFIP Advances in Information and Communication Technology</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1007/978-3-662-45504-3_22">10.1007/978-3-662-45504-3_22</a></span>
kaust.grant.numberKUK-C1-013-04
orcid.authorPestana, Jennifer
Files