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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics, Liaoning University, Shenyang, 110036, China

    Peng Xia

  2. Automated Reasoning and Cognition Key Laboratory of Chongqing, Chongqing, 401122, China

    Peng Xia

  3. School of Mathematics, Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education), Jilin University, Changchun, 130012, China

    Shugong Zhang, Na Lei & Zhangyong Kim

Authors
  1. Peng Xia
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  2. Shugong Zhang
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  3. Na Lei
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  4. Zhangyong Kim
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Corresponding author

Correspondence to Na Lei.

Additional information

This research was supported by the National Science Foundation of China under Grant No. 11171133 and the Open Fund of Automated Reasoning and Cognition Key Laboratory of Chongqing under Grant No. CARC2014001.

This paper was recommended for publication by Editor LI Ziming.

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Xia, P., Zhang, S., Lei, N. et al. The Fitzpatrick-Neville-type algorithm for multivariate vector-valued osculatory rational interpolation. J Syst Sci Complex 28, 222–242 (2015). https://doi.org/10.1007/s11424-015-2202-9

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  • DOI: https://doi.org/10.1007/s11424-015-2202-9

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