摘要
在文[1]中AI—DING BIEN与FUHUA CHENG对给定的节点序列τ={τ_1}引入了一种k次交错样条G_(1,k+1)的定义,它在不同的区间[τ_l,τ_(l+1)]上交错地取k次及k—1次多项式,本文在节点不相重的条件下定义一种新的交错样条H_(i,k+1),它在不同的区间上交错地取k次、k-1次……及零次多项式,及其与普通的B样条的关系。更一般地给定一组非负整数0≤k_1<k_2<……<k_p=k我们给出交错地取k_p次、k_(p-1)次……及k_1次多项式的交错样条J_(i,k+1)的构造方法。
Let τ= {τ_1} be a knot sequence without multiple knots. This paper gives anew alternate spline of degree k, H_(1,k+1), for which degrees or polynomials canbe alternately taken from k until o in different intervals [τ_i, τ_(1+1)]. And wealso discuss relation between H_(1, k+1) and B -- splines. More generally, let 0≤k_1<k_2<…<k_p = k be a given set of nonnegative integers, we construct alternatesplines of degree k, J_(i, k+1), which take polynomials of degree k_p, k_(p-1),…,k_1in different intervals.
