Leverrierʹs algorithm for orthogonal polynomial bases Original Research Article

The Leverrier-Fadeev algorithm for simultaneous computation of the adjoint B(λ) and determinant a(λ) of the characteristic matrix λI − A is extended to the case when both B(λ) and a(λ) are expressed relative to a basis of orthogonal polynomials. Specific formulae are derived for the cases of Chebyshev, Hermite, Legendre, and Laguerre polynomials.