广义样条的递推式

多项式样条空间最重要的性质之一是它具有B样条基。这种B样条基能借助递推公式进行有效而精确的计算。1]证明了三角样条空间也有满足类似递推式的B样条。2]称双曲B样条也有这种递推式,其结果4]最近才发表。 对于各种广义样条空间,诸如Tchebysheff样条空间,L样条空间,Lg样条空间等,都能构造具有局部支集的基。但这些基能否用递推式加以计算的问题一直未能解决。

ON RECURRENCE RELATIONS OF GENERALIZED B-SPLINES

The bases of local-support functions for spaces of generalized splines have alreadybeen constructed. But the problem when these basis elements have recurrence relationsremains unsolved. We consider a space of generalized splines defined in 2]. 2] has proposed twokinds of reasonable recursions and obtained corresponding results. The aim of thispaper is to improve the theorems in 2].