An Algorithm for Generalized Matrix Eigenvalue Problems

摘要

A new method, called the QZ algorithm, is presented for the solution of the matrix eigenvalue problem Ax = lambda Bx with the 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 powers of lambda are also mentioned. (Author)