Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse symmetric matrices

Abstract

A band Lanczos algorithm for the iterative computation of eigenvalues and eigenvectors of a large sparse symmetric matrix is described and tested on numerical examples. It starts with a p dimensional subspace, and computes an orthonormal basis for the Krylov spaces of A, generated from this starting subspace, in which A is represented by a 2 p + 1 2p + 1 band matrix, whose eigenvalues can be computed. Special emphasis is given to devising an implementation that gives a satisfactory numerical orthogonality, with a simple program and few arithmetic operations.