An Arrmldi Code for Computing Selected Eigenvalues of Sparse, Real, Unsymmetric Matrices

Arnoldi methods can be more effective than subspace iteration methods for computing the dominant elgenvalues of a large, sparse, real, unsymmetric matrix A code, EB12, for the sparse, unsymmetrlc elgenvalue problem based on a subspace iteration algorithm, optionally combined with Chebychev acceleration, has recently been described by Duff and Scott and is included m the Harwell Subroutine Library. In this article we consider variants of the method of Arnoldl and discuss the design and development of a code to implement these methods. Tbe new code, which is called EB13, offers the user the choice of a basic Arnoldi algorlthm, an Arnoldl algorithm with Chebychev acceleration. and a Chebychev preconditioned Arnoldi algorlthm. Each method is available in blocked and unblocked form The code may be used to compute either the rightmost eigenvalues, the eigenvalues of largest absolute value, or the eigenvalues of largest imaginary part. The performance of each option m the EB13 package M compared with that of subspace Iteration on a range of test problems, and on the basis of the results, advice is offered to the user on the appropriate choice of method