Approximation order of bivariate spline interpolation for arbitrary smoothness

摘要

By using the algorithm of Nurnberger and Riessinger (1995), we construct Hermite interpolation sets for spaces of bivariate splines S_q~r(⊿~1) of arbitrary smoothness defined on the uniform type triangulations. It is shown that our Hermite interpolation method yields optimal approximation order for q ≥ 3.5r + 1. In order to prove this, we use the concept of weak interpolation and arguments of Birkhoff interpolation.