Iterative methods for the computation of a few eigenvalues of a large symmetric matrix

The task of computing a few eigenvalues and associated eigenvectors of a large sparse symmetric matrix arises in many applications. We present new iterative methods designed for the determination of a few extreme or non-extreme eigenvalues and associated eigenvectors. Our methods are based on the recursion formulas of the Implicitly Restarted Lanczos method introduced by Sorensen [1992], but differ from previous applications of these formulas in the selection of accelerating polynomial. The methods of the present paper require very little computer storage. Numerical examples illustrate that the methods can give rapid convergence.