A spectral approach to polynomial matrices solvents

A contour integral approach to the computation of invariant pairs

“…The work in [19] uses interval arithmetic to compute an interval matrix containing the exact solution to the quadratic matrix equation. For the case of the general matrix solvent problem, we can also cite [9], [30] and [23]. On the other hand, the question of designing symbolic algorithms for computing solvents remains relatively unexplored.…”

On Solvents of Matrix Polynomials

“…In a similar manner, we will establish that a left solvent ∈ can be constructed from a set {λ 1¸ λ 2¸ …, λ m } of m latent roots and a corresponding set of m linearly independent left latent (row) vectors {Y 1 where the latent roots are {0, 1, -1, -2, -3} with 0 being a double root. The right latent vectors corresponding to these latent roots are respectively:…”

“…This fact has led to an active research effort in matrix polynomials theory. A theoretical introduction based on spectral approach of matrix polynomial theory is given in [1]; the same authors proposed an algorithm based on Jordan chains for the computation of a solvent of a matrix polynomial. Methods and algorithms for numerical solutions of spectral problems for one-and two-parameter polynomial and rational matrices are given in [2].…”

“…or (1) where N r D r N l D l are matrix polynomials. This fact has led to an active research effort in matrix polynomials theory.…”