Some Remarks on the Elman Estimate for GMRES

Some Remarks on the Elman Estimate for GMRES

Starting from a GMRES error estimate proposed by Elman in terms of the ratio of the smallest eigenvalue of the hermitian part and the norm of some nonsymmetric matrix, we propose some asymptotically tighter bound in terms of the same ratio. Here we make use of a recent deep result of Crouzeix and ot...

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Veröffentlicht in:SIAM journal on matrix analysis and applications 2005-01, Vol.27 (3), p.772-778
Hauptverfasser: Beckermann, B., Goreinov, S. A., Tyrtyshnikov, E. E.
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Estimates
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Zusammenfassung:Starting from a GMRES error estimate proposed by Elman in terms of the ratio of the smallest eigenvalue of the hermitian part and the norm of some nonsymmetric matrix, we propose some asymptotically tighter bound in terms of the same ratio. Here we make use of a recent deep result of Crouzeix and others on the norm of functions of matrices.
ISSN:0895-4798
1095-7162
DOI:10.1137/040618849