Optimal a priori error bounds for the Rayleigh-Ritz method

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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Bibliographic Details
Published in:Mathematics of computation 2003-04, Vol.72 (242), p.677-684
Main Authors: SLEIJPEN, Gerard L. G, VAN DEN ESHOF, Jasper, SMIT, Paul
Format: Article
Language:English
Subjects:
A priori knowledge
Approximation
Calculus of variations and optimal control
Eigenvalues
Eigenvectors
Error bounds
Exact sciences and technology
Mathematical analysis
Mathematical vectors
Mathematics
Matrices
Numbers
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Rayleigh Ritz method
Sciences and techniques of general use
Spectral theory
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Summary: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.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-02-01435-7