0382221 - ÚI 2013 RIV US eng J - Journal Article
Duintjer Tebbens, Jurjen - Meurant, G.
Any Ritz Value Behavior Is Possible for Arnoldi and for GMRES.
SIAM Journal on Matrix Analysis and Applications. Roč. 33, č. 3 (2012), s. 958-978. ISSN 0895-4798. E-ISSN 1095-7162
R&D Projects: GA AV ČR IAA100300802
Grant - others:GA AV ČR(CZ) M100300901
Institutional research plan: CEZ:AV0Z10300504
Keywords : Ritz values * Arnoldi process * Arnoldi method * GMRES method * prescribed convergence * interlacing properties
Subject RIV: BA - General Mathematics
Impact factor: 1.342, year: 2012

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.
Permanent Link: http://hdl.handle.net/11104/0212509