An extension of Leverrier-Faddeev algorithm using a basis of classical orthogonal polynomials

Abstract

In this paper, the Leverrier-Faddeev algorithm is extended in order to compute both the determinant a(s) and the adjoint B(s) of the polynomial matrix s^pA_p + s^p-1A_p-1 + ... + sA_1 + A_0, where A_i ∈ Cnxn; i = 1, 2, ..., p. B(s) and a(s) are expressed in terms of a basis of classical orthogonal polynomials.