On Stable Local Bases for Bivariate Polynomial Spline Spaces

Abstract.

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.