A fully parallel method for tridiagonal eigenvalue problem

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.

Keywords

• eigenvalues
• eigenvalue curves
• multiprocessors
• homotopy method.