%0 Conference Proceedings
%T Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems
%+ University of Oxford
%A Pestana, Jennifer
%< avec comité de lecture
%( IFIP Advances in Information and Communication Technology
%B 26th Conference on System Modeling and Optimization (CSMO)
%C Klagenfurt, Austria
%Y Christian Pötzsche
%Y Clemens Heuberger
%Y Barbara Kaltenbacher
%Y Franz Rendl
%I Springer Berlin Heidelberg
%3 System Modeling and Optimization
%V AICT-443
%P 230-236
%8 2013-09-09
%D 2013
%R 10.1007/978-3-662-45504-3_22
%K GMRES
%K Convergence
%K Ill-posed problem
%Z Computer Science [cs]Conference papers
%X 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.
%G English
%Z TC 7
%2 https://inria.hal.science/hal-01286418/document
%2 https://inria.hal.science/hal-01286418/file/978-3-662-45504-3_22_Chapter.pdf
%L hal-01286418
%U https://inria.hal.science/hal-01286418
%~ IFIP
%~ IFIP-AICT
%~ IFIP-TC
%~ IFIP-AICT-443
%~ IFIP-TC7