Use of the Lanczos Method for Finding Complete Sets of Eigenvalues of Large Sparse Symmetric Matrices

Abstract

A way of using the Lanczos method to find all the eigenvalues of a large sparse symmetric matrix is described, and some empirical observations on the manner in which the method works in practice are given. The method seems to be accurate, fast, and not very demanding on storage. A formula for the number of iterations necessary to get the eigenvalues is proposed.