Parallel Solution of Generalized Symmetric Tridiagonal Eigenvalue Problems on Shared Memory Multiprocessors
Ribbens, Calvin J.
Beattie, Christopher A.
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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 . The second algorithm is a straightforward parallel extension of the bisection/inverse iteration algorithm treeps of Lo, Philippe, and Sameh . 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.