On Harmonic Ritz vectors and the stagnation of GMRES
arXiv:1902.08049h-index: 2
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Provides theoretical insight into GMRES stagnation for researchers in numerical linear algebra.
The paper derives necessary and sufficient conditions for the stagnation of GMRES based on harmonic Ritz vectors, extending prior work on harmonic Ritz values.
This paper derives a necessary and sufficient condition for the coincidence of Harmonic residual vectors and the residual vector in GMRES. The properties of the harmonic Ritz values at the stagnation of GMRES were described in the Proposition-4.2 of [1]. Necessary and sufficient conditions basing on Harmonic Ritz vectors for the stagnation have derived in this paper.