Leverrier–Chebyshev algorithm for the singular pencils

AbstractThe 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)≢0. 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