LZ-ALGORITHM TO SOLVE GENERALIZED EIGENVALUE PROBLEM

An algorithm for finding x and lambda such that Ax equals lambda Bx, where A and B are n multiplied by n matrices is presented and analyzed. The algorithm does not require matrix inversion, and may be used when either or both matrices are singular. The method is a generalization of H. Rutishauser's LR-method for the standard eigenvalue problem Ax equals lambda x and closely resembles the QZ-algorithm given by C. B. Moler and G. W. Stewart for the generalized problem given above. Unlike the QZ-algorithm, which uses orthogonal transformations, the LZ-algorithm uses elementary transformations and should be more efficient when A or B is complex.