Finding eigenvalues and eigenvectors of unsymmetric matrices using a hypercube multiprocessor

Abstract

Distributed-memory algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric systems, little work has been done on the unsymmetric case. Our parallel implementation proceeds in three major steps: reduction of the original matrix to Hessenberg form, application of the implicit double-shift QR algorithm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication and pipelining, are discussed and compared. Results and timings are given.