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Publicly Available Published by De Gruyter July 11, 2013

A Short Theory of the Rayleigh–Ritz Method

  • Harry Yserentant EMAIL logo

Abstract.

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.

Published Online: 2013-07-11
Published in Print: 2013-10-01

© 2013 by Walter de Gruyter Berlin Boston

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