An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems

Abstract

In this paper, we present an inverse free Krylov subspace method for finding some extreme eigenvalues of the symmetric definite generalized eigenvalue problem $Ax = \lambda B x$. The basic method takes a form of inner-outer iterations and involves no inversion of B or any shift-and-invert matrix $A-\lambda_0 B$. A convergence analysis is presented that leads to a preconditioning scheme for accelerating convergence through some equivalent transformations of the eigenvalue problem. Numerical examples are given to illustrate the convergence properties and to demonstrate the competitiveness of the method.