Parallel Spectral Division Using the Matrix Sign Function for the Generalized Eigenproblem

Abstract

In this paper we demonstrate the parallelism of the spectral division using the matrix sign function for the generalized nonsymmetric eigenproblem. We employ the so–called generalized Newton iterative scheme in order to compute the sign function of the matrix pair. A recent study showed a considerable reduction (by 75%) in the computational cost of this iteration, making this approach competitive when compared to the traditional QZ algorithm. The experimental results on an IBM SP3 multicomputer report the parallel performance (efficiency around 60–80%) and scalability of this approach.