A note on constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain

In the paper [H.S. Kim, Y.J. Ahn, Constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain, J. Comput. Appl. Math. 216 (2008) 14–19], Kim and Ahn proved that the best constrained degree reduction of a polynomial over d -dimensional simplex domain in L 2 -norm equals the best approximation of weighted Euclidean norm of the Bernstein–Bézier coefficients of the given polynomial. In this paper, we presented a counterexample to show that the approximating polynomial of lower degree to a polynomial is virtually non-existent when d ≥ 2 . Furthermore, we provide an assumption to guarantee the existence of solution for the constrained degree reduction.