A Newtonian procedure for the solutions of Ex = λAx

Newtonian iteration on a scalar function, which is obtained by condensation of the pencil E - λA, is used in conjunction with Sturm sequence properties of the pencil to provide an infallible, quadratically convergent algorithm for all eignevalues of A^-1E within any stated λ-range. The algorithm has been programmed for use on a desk-top machine and large (sparse matrix) eigenvalue problems have been solved. A brief outline of the essential steps in the program is given along with some particular solutions.