International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 741-752

A fully parallel method for tridiagonal eigenvalue problem

Kuiyuan Li

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.


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.