[en] In this paper an iterative technique is discussed for finding the algebraic alloy smallest (or largest) eigenvalue of the generalized eigenvalue problem. A-lambda M, where A and M are real, symmetric, and M is positive definite. It is assumed that A and M are such that it is undesirable to factor the matrix A-sigma M for any value of sigma. It is proved that the algorithm is globally convergent, and that convergence is asymptotically quadratic. Finally, the modifications required in the algorithm to make it computationally feasible are discussed