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The Discrete Approximation Problem for a Special Case of Hermite-Type Polynomial Interpolation

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Abstract

Every univariate Hermite interpolation problem can be written as a pointwise limit of Lagrange interpolants. However, this property is not preserved for the multivariate case. In this paper, the authors first generalize the result of P. Gniadek. As an application, the authors consider the discrete approximation problem for a special case when the interpolation condition contains all partial derivatives of order less than n and one nth order differential polynomial. In addition, for the case of n ≥ 3, the authors use the concept of Cartesian tensors to give a sufficient condition to find a sequence of discrete points, such that the Lagrange interpolation problems at these points converge to the given Hermite-type interpolant.

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Author information

Authors and Affiliations

  1. College of Science, Northeast Electric Power University, Jilin, 132000, China

    Yihe Gong

  2. School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang, 110034, China

    Xue Jiang

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

    Shugong Zhang

Authors
  1. Yihe Gong
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  2. Xue Jiang
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  3. Shugong Zhang
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Corresponding author

Correspondence to Xue Jiang.

Additional information

This paper was supported by the National Natural Science Foundation of China under Grant Nos. 11901402 and 11671169.

This paper was recommended for publication by Editor WU Wenyuan.

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Gong, Y., Jiang, X. & Zhang, S. The Discrete Approximation Problem for a Special Case of Hermite-Type Polynomial Interpolation. J Syst Sci Complex 35, 2004–2015 (2022). https://doi.org/10.1007/s11424-022-1068-x

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  • DOI: https://doi.org/10.1007/s11424-022-1068-x

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