Some Remarks on the Elman Estimate for GMRES
- 1 January 2005
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 27 (3), 772-778
- https://doi.org/10.1137/040618849
Abstract
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.Keywords
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