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

GONG Yihe1, JIANG Xue2, ZHANG Shugong3

1. 1. College of Science, Northeast Electric Power University, Jilin 132000, China;
2. School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China;
3. Institute of Mathematics, Key Lab. of Symbolic Computation and Knowledge Engineering (Ministry of Education), Jilin University, Changchun 130012, China
• Received:2021-03-12 Revised:2021-05-17 Online:2022-10-25 Published:2022-10-12
• Supported by:
This paper was supported by the National Natural Science Foundation of China under Grant Nos.11901402 and 11671169.

GONG Yihe, JIANG Xue, ZHANG Shugong. The Discrete Approximation Problem for a Special Case of Hermite-Type Polynomial Interpolation[J]. Journal of Systems Science and Complexity, 2022, 35(5): 2004-2015.

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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