Restarted simpler GMRES augmented with harmonic Ritz vectors
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Computing smallest singular triplets with implicitly restarted Lanczos bidiagonalization
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
A modified harmonic block Arnoldi algorithm with adaptive shifts for large interior eigenproblems
Journal of Computational and Applied Mathematics
Incremental spectral preconditioners for sequences of linear systems
Applied Numerical Mathematics
An invert-free Arnoldi method for computing interior eigenpairs of large matrices
International Journal of Computer Mathematics
Applied Numerical Mathematics
Restarted weighted full orthogonalization method for shifted linear systems
Computers & Mathematics with Applications
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Minimizing communication in sparse matrix solvers
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Adaptive preconditioners for nonlinear systems of equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Toward memory-efficient linear solvers
VECPAR'02 Proceedings of the 5th international conference on High performance computing for computational science
SIAM Journal on Scientific Computing
The Iterative Solver RISOLV with Application to the Exterior Helmholtz Problem
SIAM Journal on Scientific Computing
Flexible GMRES with Deflated Restarting
SIAM Journal on Scientific Computing
GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem
Applied Numerical Mathematics
GMRES implementations and residual smoothing techniques for solving ill-posed linear systems
Computers & Mathematics with Applications
Analysis of an implicitly restarted simpler GMRES variant of augmented GMRES
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part II
A new shift scheme for the harmonic Arnoldi method
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
SIAM Journal on Matrix Analysis and Applications
Original Article: Simpler GMRES with deflated restarting
Mathematics and Computers in Simulation
Numerical Algorithms
Journal of Computational and Applied Mathematics
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The generalized minimum residual method (GMRES) is well known for solving large nonsymmetric systems of linear equations. It generally uses restarting, which slows the convergence. However, some information can be retained at the time of the restart and used in the next cycle. We present algorithms that use implicit restarting in order to retain this information. Approximate eigenvectors determined from the previous subspace are included in the new subspace. This deflates the smallest eigenvalues and thus improves the convergence. The subspace that contains the approximate eigenvectors is itself a Krylov subspace, but not with the usual starting vector. The implicitly restarted FOM algorithm includes standard Ritz vectors in the subspace. The eigenvalue portion of its calculations is equivalent to Sorensen's IRA algorithm. The implicitly restarted GMRES algorithm uses harmonic Ritz vectors. This algorithm also gives a new approach to computing interior eigenvalues.