An Algorithm for Generalized Matrix Eigenvalue Problems

A new method, called the QZ algorithm, is presented for the solution of the matrix eigenvalue problem Ax = Bx with general square matrices A and B. Particular attention is paid to the degeneracies which result when B is singular. No inversions of B or its submatrices are used. The algorithm is a generalization of the QR algorithm, and reduces to it when B = I. Problems involving higher powers of are also mentioned.