Optimal a priori error bounds for the Rayleigh-Ritz method

Authors:
Gerard L. G. Sleijpen;Jasper van den Eshof;Paul Smit
Affiliations:
Department of Mathematics, Utrecht University, P.O. Box 80.101, NL-3508 TA Utrecht, The Netherlands;Department of Mathematics, Utrecht University, P.O. Box 80.101, NL-3508 TA Utrecht, The Netherlands;IBM, Watsonweg 2, 1423 ND, Uithoorn, The Netherlands and Center for Economic Research, Tilburg University, Tilburg, The Netherlands
Venue:
Mathematics of Computation
Year:
2003

Citing 3
Cited 0

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Abstract

We derive error bounds for the Rayleigh-Ritz method for the approximation to extremal eigenpairs of a symmetric matrix. The bounds are expressed in terms of the eigenvalues of the matrix and the angle between the subspace and the eigenvector. We also present a sharp bound.