Abstract : 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.
https://hal.inria.fr/hal-01286418 Contributor : Hal IfipConnect in order to contact the contributor Submitted on : Thursday, March 10, 2016 - 5:19:14 PM Last modification on : Thursday, March 5, 2020 - 4:31:59 PM Long-term archiving on: : Sunday, November 13, 2016 - 3:26:39 PM
Jennifer Pestana. Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. pp.230-236, ⟨10.1007/978-3-662-45504-3_22⟩. ⟨hal-01286418⟩