Any Ritz Value Behavior Is Possible for Arnoldi and for GMRES
Authors:
- Jurjen Duintjer TebbensJTJurjen Duintjer Tebbens
- Gérard MeurantGMGérard Meurant
- 1 January 2012
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 33 (3) , 958-978
Abstract
We show that arbitrary convergence behavior of Ritz values is possible in the Arnoldi method, and we give two parametrizations of the class of matrices with initial Arnoldi vectors that generate prescribed Ritz values (in all iterations). The second parametrization enables us to prove that any GMRES residual norm history is possible with any prescribed Ritz values (in all iterations), provided that we treat the stagnation case appropriately.Keywords
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