On Stable Local Bases for Bivariate Polynomial Spline Spaces

Stable locally supported bases are constructed for the spaces cal S _d ^r (triangle) of polynomial splines of degree d≥ 3r+2 and smoothness r defined on triangulations triangle , as well as for various superspline subspaces. In addition, we show that for r≥ 1 , in general, it is impossible to construct bases which are simultaneously stable and locally linearly independent. February 2, 2000. Date revised: November 27, 2000. Date accepted: March 7, 2001.