Polynomial degree reduction in the discrete $$L_2$$ L 2 -norm equals best Euclidean approximation of h-Bézier coefficients

Abstract

We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete $$L_2$$ -norm is equivalent to the best Euclidean distance of the vector of h-Bezier coefficients of P from the vector of degree raised h-Bezier coefficients of polynomials of degree m. Moreover, we demonstrate the adequacy of h-Bezier curves for approaching the problem of weighted discrete least squares approximation. Applications to discrete orthogonal polynomials are also presented.