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

Handle URI:
http://hdl.handle.net/10754/599513
Title:
Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems
Authors:
Pestana, Jennifer
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.
Citation:
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.
Publisher:
Springer Science + Business Media
Journal:
IFIP Advances in Information and Communication Technology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
2014
DOI:
10.1007/978-3-662-45504-3_22
Type:
Book Chapter
ISSN:
1868-4238; 1868-422X
Sponsors:
This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorPestana, Jenniferen
dc.date.accessioned2016-02-28T05:52:32Zen
dc.date.available2016-02-28T05:52:32Zen
dc.date.issued2014en
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.en
dc.identifier.issn1868-4238en
dc.identifier.issn1868-422Xen
dc.identifier.doi10.1007/978-3-662-45504-3_22en
dc.identifier.urihttp://hdl.handle.net/10754/599513en
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.en
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).en
dc.publisherSpringer Science + Business Mediaen
dc.subjectConvergenceen
dc.subjectGMRESen
dc.subjectIll-posed problemen
dc.titleRight-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problemsen
dc.typeBook Chapteren
dc.identifier.journalIFIP Advances in Information and Communication Technologyen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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