International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 11, Pages 74507, 13 p.
doi:10.1155/IJMMS/2006/74507

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

Abstract

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 sE−A where E is a singular matrix but det⁡(sE−A)≢0. Using a previous result by the authors we express B(s) and det⁡(sE−A) in terms of classical orthogonal polynomials.