A computer-aided method for solvents and spectral factors of matrix polynomials

Abstract

A new approach for determining the complete sets of solvents and spectral factors of a monic matrix polynomial is proposed. A systematic method for determining the initial guess for the extended multidimensional Newton-Raphson method is first proposed, such that the eigenspectrum corresponding to each solvent of the matrix polynomial can be determined. With the evaluated eigenspectra, complete sets of solvents and spectral factors of a monic matrix polynomial can be obtained by utilizing the applications and the advantages of the principal- nth-root method, the matrix sign function, and the block-power method. The established algorithms can be applied in the analysis and/or design of systems described by high-degree vector differential equations and/or matrix fractions.