Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems
Type
Book ChapterAuthors
Pestana, JenniferKAUST Grant Number
KUK-C1-013-04Date
2014-11-28Online Publication Date
2014-11-28Print Publication Date
2014Permanent link to this record
http://hdl.handle.net/10754/599513
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Show full item recordAbstract
© 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.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).Publisher
Springer Natureae974a485f413a2113503eed53cd6c53
10.1007/978-3-662-45504-3_22