Some Remarks on the Elman Estimate for GMRES
Bernhard Beckermann, S. A. Goreinov, E. E. Tyrtyshnikov · SIAM Journal on Matrix Analysis and Applications · 2005
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.