Parallel Computation of Pseudospectra Using Transfer Functions on a MATLAB-MPI Cluster Platform
Proceedings of the 9th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface
Accurate conjugate gradient methods for families of shifted systems
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
Extended Krylov subspace for parameter dependent systems
Applied Numerical Mathematics
Solution of generalized shifted linear systems with complex symmetric matrices
Journal of Computational Physics
Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems
SIAM Journal on Matrix Analysis and Applications
Dissecting the FEAST algorithm for generalized eigenproblems
Journal of Computational and Applied Mathematics
Accelerated GCRO-DR method for solving sequences of systems of linear equations
Journal of Computational and Applied Mathematics
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Shifted matrices, which differ by a multiple of the identity only, generate the same Krylov subspaces with respect to any fixed vector. This fact has been exploited in Lanczos-based methods like CG, QMR, and BiCG to simultaneously solve several shifted linear systems at the expense of only one matrix--vector multiplication per iteration. Here, we develop a variant of the restarted GMRES method exhibiting the same advantage and we investigate its convergence for positive real matrices in some detail. We apply our method to speed up "multiple masses" calculations arising in lattice gauge computations in quantum chromodynamics, one of the most time-consuming supercomputer applications.