Perturbed Arnoldi Method for Computing Multiple Eigenvalues
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There are several known methods for computing eigenvalues of a large sparse nonsymmetric matrix. One of the most efficient methods is known as the Arnoldi method. The Arnoldi method is a Krylov subspace method that computes the eigenvalues of the projection of a matrix onto the Krylov subspace. In our investigation, we present both non-restarted and restarted Arnoldi methods and examine how round-off error helps find multiple eigenvalues. We introduce a new method that uses a diagonal matrix perturbation that separates multiple eigenvalues and improves performance. Our approach presents an alternative that avoids the need for a block method, or for relying on round-off error to introduce multiple copies of eigenvalues.