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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year

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Volume 13, Issue 4


A Short Theory of the Rayleigh–Ritz Method

Harry Yserentant
Published Online: 2013-07-11 | DOI: https://doi.org/10.1515/cmam-2013-0013


We present some new error estimates for the eigenvalues and eigenfunctions obtained by the Rayleigh–Ritz method, the common variational method to solve eigenproblems. The errors are bounded in terms of the error of the best approximation of the eigenfunction under consideration by functions in the ansatz space. In contrast to the classical theory, the approximation error of eigenfunctions other than the given one does not enter into these estimates. The estimates are based on a bound for the norm of a certain projection operator, e.g., in finite element methods for second order eigenvalue problems, the H1-norm of the L2-projection onto the finite element space.

Keywords: Eigenvalues; Eigenfunctions; Error Estimates

About the article

Published Online: 2013-07-11

Published in Print: 2013-10-01

Citation Information: Computational Methods in Applied Mathematics, Volume 13, Issue 4, Pages 495–502, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2013-0013.

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