GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A theoretical comparison of the Arnoldi and GMRES algorithms
SIAM Journal on Scientific and Statistical Computing
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
Any Nonincreasing Convergence Curve is Possible for GMRES
SIAM Journal on Matrix Analysis and Applications
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
Computable Convergence Bounds for GMRES
SIAM Journal on Matrix Analysis and Applications
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
A Note on Preconditioning for Indefinite Linear Systems
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
| Hi-index | 0.00 |
We generalize and extend results of the series of papers by Greenbaum and Strakoš (IMA Vol Math Appl 60:95---118, 1994), Greenbaum et al. (SIAM J Matrix Anal Appl 17(3):465---469, 1996), Arioli et al. (BIT 38(4):636---643, 1998) and Duintjer Tebbens and Meurant (SIAM J Matrix Anal Appl 33(3):958---978, 2012). They show how to construct matrices with right-hand sides generating a prescribed GMRES residual norm convergence curve as well as prescribed Ritz values in all iterations, including the eigenvalues, and give parametrizations of the entire class of matrices and right-hand sides with these properties. These results assumed that the underlying Arnoldi orthogonalization processes are breakdown-free and hence considered non-derogatory matrices only. We extend the results with parametrizations of classes of general nonsingular matrices with right-hand sides allowing the early termination case and also give analogues for the early termination case of other results related to the theory developed in the papers mentioned above.