Prescribing the behavior of early terminating GMRES and Arnoldi iterations

0390278 - ÚI 2014 RIV NL eng J - Článek v odborném periodiku
Duintjer Tebbens, Jurjen - Meurant, G.
Prescribing the behavior of early terminating GMRES and Arnoldi iterations.
Numerical Algorithms. Roč. 65, č. 1 (2014), s. 69-90. ISSN 1017-1398. E-ISSN 1572-9265
Grant CEP: GA AV ČR IAA100300802
Grant ostatní: GA AV ČR(CZ) M100301201
Výzkumný záměr: CEZ:AV0Z10300504
Klíčová slova: Arnoldi process * early termination * GMRES method * prescribed GMRES convergence * Arnoldi method * prescribed Ritz values
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.417, rok: 2014

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.
Trvalý link: http://hdl.handle.net/11104/0219143