Classical orthogonal polynomials and Leverrier-Faddeev algorithm for the matrix pencilssE−A

Abstract

In this contribution we present an extension of the Leverrier-Faddeev algorithm for the simultaneous computation of the determinant and the adjoint matrixB(s)of a pencilsE−AwhereEis a singular matrix butdet⁡(sE−A)≢0. Using a previous result by the authors we expressB(s)anddet⁡(sE−A)in terms of classical orthogonal polynomials.