A PROCESS FOR SOLVING A FEW EXTREME EIGENPAIRS OF LARGE SPARSE POSITIVE DEFINITE GENERALIZED EIGENVALUE PROBLEM

摘要

In this paper, an algorithm for computing some of the largest (smallest) gener- alized eigenvalues with corresponding eigenvectors of a sparse symmetric positive definite matrix pencil is presented. The algorithm uses an iteration function and inverse power iteration process to get the largest one first, then executes m-1 Lanczos-like steps to get initial approximations of the next m-1 ones, without Computing any Ritz pair, for which a procedure combining Rayleigh quotient itera- tion with shifted inverse power iteration is used to obtain more accurate eigenvalues And eigenvectors.