Any Admissible Harmonic Ritz Value Set is Possible for GMRES

0477885 - ÚI 2018 RIV US eng J - Journal Article
Du, K. - Duintjer Tebbens, Jurjen - Meurant, G.
Any Admissible Harmonic Ritz Value Set is Possible for GMRES.
Electronic Transactions on Numerical Analysis. Roč. 47, September 18 (2017), s. 37-56. ISSN 1068-9613. E-ISSN 1068-9613
R&D Projects: GA ČR GA13-06684S
Institutional support: RVO:67985807
Keywords : Ritz values * harmonic Ritz values * GMRES convergence * prescribed residual norms * FOM convergence
OECD category: Applied mathematics
Impact factor: 1.138, year: 2017
http://etna.mcs.kent.edu/volumes/2011-2020/vol47/abstract.php?vol=47&pages=37-56

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.
Permanent Link: http://hdl.handle.net/11104/0274104