Relaxation strategies for nested Krylov methods
Journal of Computational and Applied Mathematics
Linear multifrequency-grey acceleration recast for preconditioned Krylov iterations
Journal of Computational Physics
Limiting accuracy of segregated solution methods for nonsymmetric saddle point problems
Journal of Computational and Applied Mathematics
ACM Transactions on Mathematical Software (TOMS)
Constraint Schur complement preconditioners for nonsymmetric saddle point problems
Applied Numerical Mathematics
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High Performance Computing for Computational Science - VECPAR 2008
Journal of Scientific Computing
Relaxation strategies for nested Krylov methods
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
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ACM SIGGRAPH Asia 2010 papers
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
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SIAM Journal on Scientific Computing
Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential
SIAM Journal on Scientific Computing
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SIAM Journal on Scientific Computing
Stochastic computing: embracing errors in architectureand design of processors and applications
CASES '11 Proceedings of the 14th international conference on Compilers, architectures and synthesis for embedded systems
Restarted GMRES with inexact matrix–vector products
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
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Euro-Par'11 Proceedings of the 2011 international conference on Parallel Processing - Volume 2
SIAM Journal on Matrix Analysis and Applications
Self-stabilizing iterative solvers
ScalA '13 Proceedings of the Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems
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We provide a general framework for the understanding of inexact Krylov subspace methods for the solution of symmetric and nonsymmetric linear systems of equations, as well as for certain eigenvalue calculations. This framework allows us to explain the empirical results reported in a series of CERFACS technical reports by Bouras, Frayssé, and Giraud in 2000. Furthermore, assuming exact arithmetic, our analysis can be used to produce computable criteria to bound the inexactness of the matrix-vector multiplication in such a way as to maintain the convergence of the Krylov subspace method. The theory developed is applied to several problems including the solution of Schur complement systems, linear systems which depend on a parameter, and eigenvalue problems. Numerical experiments for some of these scientific applications are reported.