Parallel evaluation of leftmost eigenpairs of large unsymmetric matrices

Abstract

AbstractA parallel algorithm for the efficient calculation of m (m ⩽ 15) eigenvalues of smallest absolute magnitude for large sparse unsymmetric matrices is implemented and presented. The procedure employes a modification of the reverse simultaneous iteration scheme, which involves, among other things, the solution of m systems of linear equations. This phase is by far the most computationally demanding of the entire algorithm. However, efficient parallelization can be achieved, highly reducing the overall computational load. Numerical experiments consider the calculation of the m = 12 and m = 15 leftmost eigenvalues and eigenvectors of seven test matrices of varying size between n = 512 and n = 3564. All the computations are performed on a 4 CPU CRAY YMP8/432 machine. The accuracy of the eigenpairs found with the proposed algorithm is independent of the number of CPUs employed. Wall clock time and speed‐up measurements show that the scheme is efficient and robust and is well parallelized. In fact, average speed‐up factors of up to 3.72 were obtained. © 1994 John Wiley & Sons, Inc.