AN ANALOG FOR SZEGO POLYNOMIALS OF THE CLENSHAW ALGORITHM

Linear combinations of polynomials that are orthogonal with respect to an inner product defined on (part of) the real axis are commonly evaluated by the Clenshaw algorithm. We present an analogous algorithm for the evaluation of a linear combination SIGMA(j=0)(n)alpha(j)phi(j) of polynomials phi(j) that are orthogonal with respect to an inner product defined on (part of) the unit circle. The phi(j) are known as Szego polynomials, and find applications, e.g., in signal processing. We also discuss how to express SIGMA(j=0)(n)alpha(j)phi(j) as a linear combination of monomials.