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On stable local bases for bivariate polynomial spline spaces

Davydov, Oleg and Schumaker, Larry L. (2001) On stable local bases for bivariate polynomial spline spaces. Constructive Approximation, 18 (1). pp. 87-116. ISSN 0176-4276

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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.