Least squares approximation of Bezier coefficients provides best degree reduction in the L-2-norm

Given a polynomial p in d variables and of degree ii we want to find the be st L-2-approximation over a d-simplex from polynomials of degree m < n. Thi s problem is shown to be equivalent to the problem of finding the best Eucl idean approximation of the Bernstein-Bezier coefficients of p from the spac e of degree-raised Bernstein-Bezier coefficients of polynomials of degree m . (C) 200 Academic Press.