Convexity-Preserving Polynomial Splines of Non-uniform Degree

In this paper the problem of convexity-preserving interpolation is investigated by introducing a class of C2 polynomial splines of nonuniform degree. It is shown that as the degrees increase globally the spline converges to the linear interpolant with the best-approximation rate. An algorithm is presented for constructing C2 convexity-preserving interpolants and several numerical results are given.