| 一类多元全次数 Hermite 插值问题研究 |
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| 引用本文： | 胡忠勇,孟兆良,罗钟铉. 一类多元全次数 Hermite 插值问题研究[J]. 数学研究及应用, 2017, 37(3): 345-350 |
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| 作者姓名： | 胡忠勇 孟兆良 罗钟铉 |
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| 作者单位： | 大连理工大学数学科学学院, 辽宁 大连 116024; 泰山学院数学与统计学院, 山东 泰安 271021,大连理工大学数学科学学院, 辽宁 大连 116024,大连理工大学数学科学学院, 辽宁 大连 116024; 大连理工大学软件学院, 辽宁 大连 116620 |
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| 基金项目： | 国家自然科学基金 (Grant Nos.11301053; 61432003). |
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| 摘 要： | In this paper we study a class of multivariate Hermite interpolation problem on 2~d nodes with dimension d ≥ 2 which can be seen as a generalization of two classical Hermite interpolation problems of d = 2. Two combinatorial identities are firstly given and then the regularity of the proposed interpolation problem is proved.
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| 关 键 词： | 多元Hermite插值 正则性 全次数 |
| 收稿时间： | 2017-01-12 |
| 修稿时间： | 2017-03-15 |
A Class of Multivariate Hermite Interpolation of Total Degree |
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| Zhongyong HU,Zhaoliang MENG and Zhongxuan LUO. A Class of Multivariate Hermite Interpolation of Total Degree[J]. Journal of Mathematical Research with Applications, 2017, 37(3): 345-350 |
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| Authors: | Zhongyong HU Zhaoliang MENG Zhongxuan LUO |
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| Affiliation: | School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China; School of Mathematics and Statistics, Taishan College, Shandong 271021, P. R. China,School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China and School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China; School of Software, Dalian University of Technology, Liaoning 116620, P. R. China |
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| Abstract: | In this paper we study a class of multivariate Hermite interpolation problem on $2^d$ nodes with dimension $dgeq 2$ which can be seen as a generalization of two classical Hermite interpolation problems of $d=2$. Two combinatorial identities are firstly given and then the regularity of the proposed interpolation problem is proved. |
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| Keywords: | multivariate Hermite interpolation regularity total degree |
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