A DAVIDSON PROGRAM FOR FINDING A FEW SELECTED EXTREME EIGENPAIRS OF A LARGE, SPARSE, REAL, SYMMETRICAL MATRIX

A program is presented for determining a few,selected eigenvalues and their eigenvectors on either end of the spectrum of a large, real, symmetric matrix. Based on the Davidson method, which is extensively used in quantum chemistry/physics, the current implementation improves the power of the original algorithm by adopting several extensions. The matrix-vector multiplication routine that it requires is to be provided by the user. Different matrix formats and optimizations are thus feasible. Examples of an efficient sparse matrix representation and a matrix-vector multiplication are given. Some comparisons with the Lanczos method demonstrate the efficiency of the program.