加密网格点二元局部基插值样条函数

1.简介 由于在理论以及应用两方面的重要性,多元样条引起了许多人的注意(6],7]),紧支撑光滑分片多项式函数对于曲面的逼近是一个十分有效的工具。由于它们的局部支撑性,它们很容易求值;由于它们的光滑性,它们能被应用到要满足一定光滑条件的情况下;由于它们是紧支撑的,它们的线性包有很大的逼近灵活性,而且用它们构造逼近方法来解决的系统是

ON BIVARIATE N-SPLINE INTERPOLATION LOCAL BASIS FOR SCATTERED DATA OVER REFINED GRID POINTS

Because of its importance in both theory and applications, multivariate splines for scattered data have attracted special attentions in many fields. Based on the theory of spline functions in Hilbert spaces, bivariate polynomial natural splines for interpolating, smoothing or generalized interpolating of scattered data over an arbitary domain were constructed by the one-side functions. However, this method is not well suited for large scale numerical applications. New locally supported basis for the bivariate polynomial natural spline space to scattered data or scattered data on some lines are constructed by Guan these years. Some properties of these basis are also discussed. In this paper, locally supported functions as basis of a spline space and some properties of the basis are given to the scattered data over refined grid points. Suppose given divisions We call the gird points and the sub-grid points as refined gird points. For interpolating problems, new locally supported basis for the bivariate polynomial natural spline space to refined grid points are constructed.