VECTOR ORTHOGONAL POLYNOMIALS AND LEAST-SQUARES APPROXIMATION

We describe an algorithm for complex discrete least squares approximat ion, which turns out to be very efficient when function values are pre scribed in points on the real axis or on the unit circle. In the case of polynomial approximation, this reduces to algorithms proposed by Ru tishauser, Gragg, Harrod, Reichel, Ammar, and others. The underlying r eason for efficiency is the existence of a recurrence relation for ort hogonal polynomials, which are used to represent the solution. We show how these ideas can be generalized to least squares approximation pro blems of a more general nature.