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Optimal a priori error bounds for the Rayleigh-Ritz method


Authors: Gerard L. G. Sleijpen, Jasper van den Eshof and Paul Smit
Journal: Math. Comp. 72 (2003), 677-684
MSC (2000): Primary 65F15; Secondary 65F50
DOI: https://doi.org/10.1090/S0025-5718-02-01435-7
Published electronically: May 1, 2002
MathSciNet review: 1954961
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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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Additional Information

Gerard L. G. Sleijpen
Affiliation: Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands
Email: sleijpen@math.uu.nl

Jasper van den Eshof
Affiliation: Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands
Email: eshof@math.uu.nl

Paul Smit
Affiliation: Center for Economic Research, Tilburg University, Tilburg, The Netherlands
Address at time of publication: IBM, Watsonweg 2, 1423 ND, Uithoorn, The Netherlands
Email: p.smit@nl.ibm.com

DOI: https://doi.org/10.1090/S0025-5718-02-01435-7
Keywords: Symmetric matrices, eigenvalue problem, subspace projection, Rayleigh-Ritz, error bounds
Received by editor(s): October 18, 2000
Received by editor(s) in revised form: May 29, 2001
Published electronically: May 1, 2002
Additional Notes: The research of the second author was financially supported by the Dutch Scientific Organization (NWO), under project number 613.002.035
Article copyright: © Copyright 2002 American Mathematical Society

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