Skip Navigation

The Computer Journal 1971 14(3):263-269; doi:10.1093/comjnl/14.3.263
© 1971 by British Computer Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrow Search for citing articles in:
ISI Web of Science (6)
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Beaubien, M. J.
Right arrow Articles by Wexler, A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Iterative, finite difference solution of interior eigenvalues and eigenfunctions of Laplace's operator

M. J. Beaubien * and A. Wexler *

Numerical Applications Group, Department of Electrical Engineering, University of Manitoba, Winnipeg, Manitoba, Canada

This paper discusses and compares two iterative methods for solutions of the Helmholtz equation. Ordinary successive overrelaxation (SOR) fails to converge to eigenvalues other than the first. One convergent iterative approach investigated is the accelerated method of Kaczmarz. The other method, proposed in this paper, obtains the solution by redefining the problem such that the new system matrix is symmetric and positive semidefinite for all eigenvalues. SOR is then guaranteed to converge. The resulting matrix is the one defined by premultiplication of the original system matrix by its transpose. This cannot be done directly as excessive computer store would be required for high accuracy. An algorithm is described which produces only one row at a time of the new matrix equation, using linear combinations of a few easily generated rows of the original system, thus reserving almost all store for the eigenvector. SOR on the positive definite system (PDSOR) is then applied. Numerical results obtained indicate that PDSOR converges far more rapidly than accelerated Kaczmarz.

Received January 1969.

* Numerical Applications Group, Department of Electrical Engineering, University of Manitoba, Winnipeg, Manitoba, Canada


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.