Any Ritz Value Behavior Is Possible for Arnoldi and for GMRES
Jurjen Duintjer Tebbens, Gérard Meurant · SIAM Journal on Matrix Analysis and Applications · 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.