Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year


IMPACT FACTOR 2016: 1.097

CiteScore 2016: 1.09

SCImago Journal Rank (SJR) 2016: 0.872
Source Normalized Impact per Paper (SNIP) 2016: 0.887

Mathematical Citation Quotient (MCQ) 2016: 0.75

Online
ISSN
1609-9389
See all formats and pricing
More options …
Volume 13, Issue 4 (Oct 2013)

Issues

A Short Theory of the Rayleigh–Ritz Method

Harry Yserentant
  • Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany
  • Email:
Published Online: 2013-07-11 | DOI: https://doi.org/10.1515/cmam-2013-0013

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.

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, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2013-0013.

Export Citation

© 2013 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

Comments (0)

Please log in or register to comment.
Log in