Relaxation strategies for nested Krylov methods
Journal of Computational and Applied Mathematics
Fast iterative solution of elliptic control problems in wavelet discretization
Journal of Computational and Applied Mathematics
Limiting accuracy of segregated solution methods for nonsymmetric saddle point problems
Journal of Computational and Applied Mathematics
ACM Transactions on Mathematical Software (TOMS)
Journal of Scientific Computing
Relaxation strategies for nested Krylov methods
Journal of Computational and Applied Mathematics
Shift-Invert Arnoldi's Method with Preconditioned Iterative Solves
SIAM Journal on Matrix Analysis and Applications
Evaluation of the performance of inexact GMRES
Journal of Computational and Applied Mathematics
Restarted GMRES with inexact matrix–vector products
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
Cooperative Application/OS DRAM fault recovery
Euro-Par'11 Proceedings of the 2011 international conference on Parallel Processing - Volume 2
Self-stabilizing iterative solvers
ScalA '13 Proceedings of the Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems
A variant of IDRstab with reliable update strategies for solving sparse linear systems
Journal of Computational and Applied Mathematics
A doubly optimized solution of linear equations system expressed in an affine Krylov subspace
Journal of Computational and Applied Mathematics
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There is a class of linear problems for which the computation of the matrix-vector product is very expensive since a time consuming method is necessary to approximate it with some prescribed relative precision. In this paper we investigate the impact of approximately computed matrix-vector products on the convergence and attainable accuracy of several Krylov subspace solvers. We will argue that the sensitivity towards perturbations is mainly determined by the underlying way the Krylov subspace is constructed and does not depend on the optimality properties of the particular method. The obtained insight is used to tune the precision of the matrix-vector product in every iteration step in such a way that an overall efficient process is obtained. Our analysis confirms the empirically found relaxation strategy of Bouras and Frayssé for the GMRES method proposed in [A Relaxation Strategy for Inexact Matrix-Vector Products for Krylov Methods, Technical Report TR/PA/00/15, CERFACS, France, 2000]. Furthermore, we give an improved version of a strategy for the conjugate gradient method of Bouras, Frayssé, and Giraud used in [A Relaxation Strategy for Inner-Outer Linear Solvers in Domain Decomposition Methods, Technical Report TR/PA/00/17, CERFACS, France, 2000].