带边界条件的二元样条函数空间

ON SPACES OF BIVARIATE SPLINE FUNCTIONS WITH BOUNDARY CONDITIONS

§1.引言 本文主要讨论某一类带边界条件的二元样条函数空间的维数及其局部基函数.这方面的工作见[1—3]. 设Ω=[0,k+1]×[0,?+1].记△_(k?)~1是Ω上的三方向分划(见图1),△_(k?)~2是Ω上的四方向分划(见图2).

In this paper we study the spaces S_d^(1,1)(Δ_(kk)~i),i = 1,2, of bivariate spline functio-ns with boundary conditions on a three (and four) direction mesh.By the B-net ofthe spline function, we obtain the dimension of S_d^(1,2)(Δ_(kk)~i), i = 1,2; and a methodfor constructing a locally supported basis set for S_d^(1,1)(Δ_(kk)~i), i = 1, 2, is given. Asexamples we construct the locally supported basis set for S_4^(1,1)(Δ_kk^1) and S_3^(1,1)(Δ_(kk)~2).