Parallel Solution of Generalized Symmetric Tridiagonal Eigenvalue Problems on Shared Memory Multiprocessors

Abstract

This paper describes and compares two methods for solving a generalized eigenvalue problem , where T and S are both real symmetric and tridiagonal, and S is positive definite, and the target architecture is a shared memory multiprocessor. One method can be viewed as a generalization of the treeql algorithm of Dongarra and Sorensen [1987]. The second algorithm is a straightforward parallel extension of the bisection/inverse iteration algorithm treeps of Lo, Philippe, and Sameh [1987]. The two methods are representative of families of algorithms of quite different character. We illustrate and compare sequential and parallel performance of the two approaches with numerical examples.