【摘要】 本文选取二元五次C~2超样条函数空间作为插值空间,考虑局部Lagrange插值.首先对三角剖分△进行着色,通过Wang-加密三角剖分对原剖分△细分大约-半的三角形.然后通过在内边增加一些另外的光滑条件,使得样条函数在某些边上达到更高阶的光滑.最后在△的加密三角剖分内选择Lagrange插值点.结果表明相应的插值基函数具有局部支集.更多还原

【Abstract】 Lagrange interpolation scheme is constructed based on bivariate C~2 quintic super spline spaces on Wang’s refined triangulation.Firstly,a suitable coloring of the triangles in the original triangulation is used and about half of the triangles are subdivided by a Wang’s refined triangulation.Then,Lagrange interpolation points are chosen in the refined triangulation by requiring certain additional smoothness conditions across inserted edges.The corresponding fundamental splines have local supports.更多还原