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

Pestana, Jennifer

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

Type

Book Chapter

Authors

Pestana, Jennifer

KAUST Grant Number

KUK-C1-013-04

Online Publication Date

2014-11-28

Print Publication Date

2014

Date

2014-11-28

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.

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).