AN ARNOLDI CODE FOR COMPUTING SELECTED EIGENVALUES OF SPARSE, REAL, UNSYMMETRIC MATRICES

Arnoldi methods can be more effective than subspace iteration methods for computing the dominant eigenvalues of a large, sparse, real, unsym metric matrix. A code, EB12, for the sparse, unsymmetric eigenvalue pr oblem based on a subspace iteration algorithm, optionally combined wit h Chebychev acceleration, has recently been described by Duff and Scot t and is included in the Harwell Subroutine Library. In this article w e consider variants of the method of Arnoldi and discuss the design an d development of a code to implement these methods. The new code, whic h is called EB13, offers the user the choice of a basic Arnoldi algori thm, an Arnoldi algorithm with Chebychev acceleration, and a Chebychev preconditioned Arnoldi algorithm. Each method is available in blocked and unblocked form. The code may be used to compute either the rightm ost eigenvalues, the eigenvalues of largest absolute value, or the eig envalues of largest imaginary part. The performance of each option in the EB13 package is compared with that of subspace iteration on a rang e of test problems, and on the basis of the results, advice is offered to the user on the appropriate choice of method.