Optimal a priori error bounds for the Rayleigh-Ritz method

Sleijpen, Gerard; van den Eshof, Jasper; Smit, Paul

doi:10.1090/S0025-5718-02-01435-7

Optimal a priori error bounds for the Rayleigh-Ritz method
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by Gerard L. G. Sleijpen, Jasper van den Eshof and Paul Smit;

Math. Comp. 72 (2003), 677-684

DOI: https://doi.org/10.1090/S0025-5718-02-01435-7

Published electronically: May 1, 2002

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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.

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