FOM-inverse vector iteration method for computing a few smallest (largest) eigenvalues of pair (A, B)

In this article a new method for computing a few smallest (largest) eigenvalues of, symmetric positive definite problem, AX = λBX is presented. This is a kind of an inner–outer iteration method. The implementation of the algorithm has been tested by numerical examples, the results show that the algorithm converges fast and works with high accuracy.