TY  - JOUR
T1  - Any admissible harmonic Ritz value set is possible for GMRES
A1  - Du, Kui
A1  - Duintjer Tebbens, Jurjen
A1  - Meurant, Gérard
JA  - ETNA
Y1  - 2017
VL  - 47
SP  - 37
EP  - 56
UR  - http://etna.mcs.kent.edu/volumes/2011-2020/vol47/abstract.php?vol=47&pages=37-56
KW  - FOM convergence
KW  - GMRES convergence
KW  - harmonic Ritz values
KW  - prescribed residual norms
KW  - Ritz values
N2  - It is known that the harmonic Ritz values are the zeros of the GMRES residual polynomials. In this paper we show that any decreasing GMRES residual norm history is possible with any prescribed finite harmonic Ritz values in every iteration of the GMRES process. In addition, we characterize the admissible harmonic Ritz values when GMRES stagnates during some iterations, and show that with any prescribed, in this sense admissible harmonic Ritz values, any non-increasing GMRES residual norm history is possible. We also present a parameterization of the class of matrices and right-hand sides yielding prescribed GMRES residual norms and prescribed admissible harmonic Ritz values.
M1  - Preprint project = NCMM
M1  - Preprint year = 2017
M1  - Preprint number = 11
M1  - Preprint ID = NCMM/2017/11
ER  -