Fast inversion of Chebyshev { Vandermonde matrices 1

This paper contains two fast algorithms for inversion of ChebyshevvVander-monde matrices of the rst and second kind. They are based on special representations of the Bezoutians of Chebyshev polynomials of both kinds. The paper also contains the results of numerical experiments which show that the algorithms proposed here are not only much faster, but also more stable than other algorithms available. It is also eecient to use the above two algorithms for solving ChebyshevvVandermode systems of equations with preprocessing. 0 Introduction In this paper we consider polynomial Vandermonde matrix of the form V P t = 2 6 6 6 6 4