摘要
样条函数的精度是Schoenberg于1946年在[20]中首次提到的．本文在Schoenberg 工作的基础上,进一步讨论了这种样条的精度和跨度之间的联系,并且构造了某些特殊样条满足精度最大条件下的跨度最小．然后,我们还讨论了当一元样条的问题推广到多元的时候,如何将所要考虑的问题用多元的工具加以描述,从而能够将某些特殊的多元box样条的精度和跨度之间的联系做进一步的研究．
Spline＇s exactness is firstly mentioned in [20] by Schoenberg in 1946. In this paper, we further investigate the relationship between the spline＇exactness and its span, and construct a special spline with minimal span when its exactness reach the maximum. Then, we consider how to describe the above problem with multivariate mathematical tool when we extend the univariate case to multivariate one so that we can continuously investigate certain multivariate box splines with their exactness and span.
出处
《计算数学》
CSCD
北大核心
2006年第2期133-140,共8页
Mathematica Numerica Sinica
基金
国家自然科学基金(批准号:No.69973010
No.10271022
No.60373093)
广东省自然科学基金(批准号:No.021755)资助项目
关键词
样条精度
样条跨度
box样条
Spline＇s Exactness, Spline＇s Span, Box Spline
