The nearest polynomial of lower degree

Abstract

Suppose one is working with the polynomial p(x) = −0.99B3 0(x)−1.03B 1(x)− 0.33B 2(x) + B 3 3(x) expressed in terms of degree 3 Bernstein polynomials and suppose one has reason to believe that p(x) is really of degree 2. Applying the degree-reducing procedure [6] one gets −0.99B2 0(x)− 1.05B 1(x) + B 2(x). But is this correct, or have we treated p(x) in a Procrustean 1 fashion? Checking by converting p(x) to the power basis, we find that the coefficient of x is 0.11. Is this zero or not?