International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 74507, 13 pages

Classical orthogonal polynomials and Leverrier-Faddeev algorithm for the matrix pencils sEA

Javier Hernández and Francisco Marcellán

Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés 28911, Spain

Received 16 May 2005; Revised 27 March 2006; Accepted 25 April 2006

Copyright © 2006 Javier Hernández and Francisco Marcellán. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this contribution we present an extension of the Leverrier-Faddeev algorithm for the simultaneous computation of the determinant and the adjoint matrix B(s) of a pencil sEA where E is a singular matrix but det(sEA)0. Using a previous result by the authors we express B(s) and det(sEA) in terms of classical orthogonal polynomials.