Analysis of acceleration strategies for restarted minimal residual methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:123

Article

Eiermann, M ; Ernst, OG ; Schneider, O

关键词: Krylov subspace methods;    restarted Krylov subspace methods;    augmented Krylov subspace methods;    deflated Krylov subspace methods;    optimal truncation;    GMRES;    GMRES(m);    Ritz values;    harmonic Ritz values;    implicitly restarted Arnoldi method;   

DOI  :  10.1016/S0377-0427(00)00398-8

来源: Elsevier

【 摘 要 】

We provide an overview of existing strategies which compensate for the deterioration of convergence of minimum residual (MR) Krylov subspace methods due to restarting. We evaluate the popular practice of using nearly invariant subspaces to either augment Krylov subspaces or to construct preconditioners which invert on these subspaces. Tn the case where these spaces are exactly invariant, the augmentation approach is shown to be superior. We further show how a strategy recently introduced by de Sturler for truncating the approximation space of an MR method can be interpreted as a controlled loosening of the condition for global MR approximation based on the canonical angles between subspaces. For the special case of Krylov subspace methods, we give a concise derivation of the role of Ritz and harmonic Ritz values and vectors in the polynomial description of Krylov spaces as well as of the use of the implicitly updated Arnoldi method for manipulating Krylov spaces. (C) 2000 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free