Anzeige
Erschienen in:
2008 | OriginalPaper | Buchkapitel
Comments on the GMRES Convergence for Preconditioned Systems
verfasst von : Nabil Gmati, Bernard Philippe
Erschienen in: Large-Scale Scientific Computing
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
The purpose of this paper is to comment a frequent observation by the engineers studying acoustic scattering. It is related to the convergence of the GMRES method when solving systems
Ax
=
b
with
A
=
I
−
B
. The paper includes a theorem which expresses the convergence rate when some eigenvalues of
B
have modulus larger than one; that rate depends on the rate measured when solving the system obtained by spectral projection onto the invariant subspace corresponding to the other eigenvalues. The conclusion of the theorem is illustrated on the Helmholtz equation.