二元样条S_3~1(Δ_2)的基函数及最小支集

THE B-SPLINE BASIS AND ITS MINIMAL SUPPORT FOR THE BIVARIATE SPLINE S_3~1(△_2 )

设Δ_2是平面区域Ω=[a,b,c,d]的四方向剖分,S_3~2(Δ_2)是在Δ_2分划下的光滑度1和次数3的二元样条函数空间。利用B-网方法,我们构造了由七片多项式组成的B样条基,并证明了给B样条基具有最小支集。最后,附带给出了基函数的若干简单性质。

Let △2 be the four direction mesh on Ω= [a,b,c,d] and S31 (△2) be the space of bivariate Spline functions of smoothness 1 and degree 3 on partition △2. Using B-Net method, we have constructed the B-Spline basis which consists of seven piece polynomials and proved that the basis has minimal support. Finally,we give some simple properties of the basis.