Algorithms for solvents and spectral factors of matrix polynomials
Leang San Shieh, YIH TSONG TSAY, Norman P. Coleman · International Journal of Systems Science · 1981
A generalized Newton method, based on the contracted gradient of a matrix polynomial, is derived for solving the right (left) solvents and spectral factors of matrix polynomials. Two methods of selecting initial estimates for rapid convergence of the newly developed numerical method are proposed. Also, new algorithms for solving complete sets of the right (left) solvents and spectral factors without directly using the eigenvalues of matrix polynomials are derived. The proposed computer-aided method can be used to determine the spectral factorization of a matrix polynomial for optimal control, filtering and estimation problems.