International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 741-752
doi:10.1155/S0161171294001043
A fully parallel method for tridiagonal eigenvalue problem
Department of Mathematics and Statistics, University of West Florida, Pensacola 32514, FL, USA
Received 23 July 1992
Copyright © 1994 Kuiyuan Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, a fully parallel method for finding all eigenvalues of a real matrix pencil (A,B) is given, where A and B are real symmetric tridiagonal and B is positive definite. The method is based on the homotopy continuation coupled with the strategy ‘Divide-Conquer’ and Laguerre iterations. The numerical results obtained from implementation of this method on both single and multiprocessor computers are presented. It appears that our method is strongly competitive with other methods. The natural parallelism of our algorithm makes it an excellent candidate for a variety of advanced architectures.