GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A fast algorithm for particle simulations
Journal of Computational Physics
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
A Restarted GMRES Method Augmented with Eigenvectors
SIAM Journal on Matrix Analysis and Applications
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Analysis of Augmented Krylov Subspace Methods
SIAM Journal on Matrix Analysis and Applications
Matrix market: a web resource for test matrix collections
Proceedings of the IFIP TC2/WG2.5 working conference on Quality of numerical software: assessment and enhancement
The fast multipole method: numerical implementation
Journal of Computational Physics
Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations
SIAM Journal on Matrix Analysis and Applications
Multigrid
Residual and Backward Error Bounds in Minimum Residual Krylov Subspace Methods
SIAM Journal on Scientific Computing
GMRES with Deflated Restarting
SIAM Journal on Scientific Computing
An Analysis of Sparse Approximate Inverse Preconditioners for Boundary Integral Equations
SIAM Journal on Matrix Analysis and Applications
The Fast Multipole Method I: Error Analysis and Asymptotic Complexity
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
SIAM Journal on Scientific Computing
Modified Gram-Schmidt (MGS), Least Squares, and Backward Stability of MGS-GMRES
SIAM Journal on Matrix Analysis and Applications
Recycling Krylov Subspaces for Sequences of Linear Systems
SIAM Journal on Scientific Computing
Incremental spectral preconditioners for sequences of linear systems
Applied Numerical Mathematics
Improving the Accuracy of GMRes with Deflated Restarting
SIAM Journal on Scientific Computing
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
SIAM Journal on Matrix Analysis and Applications
Accelerated GCRO-DR method for solving sequences of systems of linear equations
Journal of Computational and Applied Mathematics
A block GCROT(m,k) method for linear systems with multiple right-hand sides
Journal of Computational and Applied Mathematics
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In many situations, it has been observed that significant convergence improvements can be achieved in preconditioned Krylov subspace methods by enriching them with some spectral information. On the other hand, effective preconditioning strategies are often designed where the preconditioner varies from one step to the next so that a flexible Krylov solver is required. In this paper, we present a new numerical technique for nonsymmetric problems that combines these two features. We illustrate the numerical behavior of the new solver both on a set of small academic test examples as well as on large industrial simulation arising in wave propagation simulations.