The Fitzpatrick-Neville-type algorithm for multivariate vector-valued osculatory rational interpolation

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• 作者：Peng Xia (1) (2)
  Shugong Zhang (3)
  Na Lei (3)
  Zhangyong Kim (3)
  
  1. School of Mathematics ; Liaoning University ; Shenyang ; 110036 ; China
  2. Automated Reasoning and Cognition Key Laboratory of Chongqing ; Chongqing ; 401122 ; China
  3. School of Mathematics ; Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education) ; Jilin University ; Changchun ; 130012 ; China
  
• 关键词：Fitzpatrick algorithm ; Gr枚bner basis ; module ; vector ; valued osculatory rational interpolation
• 刊名：Journal of Systems Science and Complexity
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：28
• 期：1
• 页码：222-242
• 全文大小：422 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory and Control
  Applied Mathematics and Computational Methods of Engineering
  Operations Research/Decision Theory
  Probability Theory and Stochastic Processes
  
• 出版者：Academy of Mathematics and Systems Science, Chinese Academy of Sciences, co-published with Springer
• ISSN：1559-7067

文摘

In this paper, the authors first apply the Fitzpatrick algorithm to multivariate vector-valued osculatory rational interpolation. Then based on the Fitzpatrick algorithm and the properties of an Hermite interpolation basis, the authors present a Fitzpatrick-Neville-type algorithm for multivariate vector-valued osculatory rational interpolation. It may be used to compute the values of multivariate vector-valued osculatory rational interpolants at some points directly without computing the interpolation function explicitly.