AN ITERATIVE SOLUTION TO THE GENERALIZED EIGENVALUE-EIGENVECTOR PROBLEM.

This paper presents an approach to the solution of what is usually called the generalized eigenvalue problem. The basic format of the method is similar to that presented by I. Tarnove, but with revisions in the root-finding and scaling procedures. The capability of calculating the associated eigenvectors has also been added to the previously-published algorithm. This method uses an iterative root-finding technique and will converge with almost any first estimate. To preserve accuracy, the original matrix is used throughout for the evaluation of the function and scaling is done by powers of two. A FORTRAN-63 program for the CDC-1604, using this method, has been written for matrices having polynomial elements. The code was evaluated using a number of trial problems, including pathological matrices, and some of these results have been incorporated into this report. Author