| 样条函数精度的某些问题研究 |
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| 引用本文： | 赵雁翔,王仁宏.样条函数精度的某些问题研究[J].计算数学,2006,28(2):133-140. |
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| 作者姓名： | 赵雁翔 王仁宏 |
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| 作者单位： | 大连理工大学数学科学研究所,大连,116024 |
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| 基金项目： | 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 |
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| 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．
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| 关 键 词： | 样条精度 样条跨度 box样条 |
| 收稿时间： | 2004-05-28 |
| 修稿时间： | 2004-05-28 |
SOME PROBLEM OF SPLINE'S EXACTNESS |
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| Zhao Yanxiang,Wang Renhong.SOME PROBLEM OF SPLINE''''S EXACTNESS[J].Mathematica Numerica Sinica,2006,28(2):133-140. |
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| Authors: | Zhao Yanxiang Wang Renhong |
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| Institution: | Institute of Mathematical Science, Dalian University of Technology, Dalian 116024, China |
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| Abstract: | 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. |
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| Keywords: | Spline's Exactness Spline's Span Box Spline |
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