Dual bases of a Bernstein polynomial basis on simplices

Abstract This paper extends the theory of dual bases of a one-variate B-spline basis to the case of Bernstein polynomials and presents methods of constructing dual bases of a Bernstein polynomial basis on a simplex from that of a one-variate polynomial basis, s{xis}ni=0 and s{Bki,k-i(x) = (ki)xi(l-x)k-i}ski=0 on the interval [0,1].