Leverrier–Chebyshev algorithm for the singular pencils Original Research Article

The Leverrier–Chebyshev algorithm is presented. It is an extension of the Leverrier–Fadeev algorithm for simultaneous computation of the adjoint B(μ) and determinant a(μ) of the singular pencil μE−A, where E is singular, but det (μE−A)not identical with0. We express the B(μ) and a(μ) relative to a basis of orthogonal Chebyshev polynomial, and as such solve a problem of S. Barnett.