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Bivariate Polynomial Interpolation over Nonrectangular Meshes

Part of: Numerical approximation and computational geometry

Published online by Cambridge University Press:  17 November 2016

Jiang Qian ,
Sujuan Zheng ,
Fan Wang  and
Zhuojia Fu
Jiang Qian*
Affiliation:
College of Sciences, Hohai University, Nanjing 211000, China
Sujuan Zheng*
Affiliation:
College of Sciences, Hohai University, Nanjing 211000, China
Fan Wang*
Affiliation:
College of Engineering, Nanjing Agricultural University, Nanjing 210031, China
Zhuojia Fu*
Affiliation:
College of Mechanics and Materials, Hohai University, Nanjing 211000, China
*
*Corresponding author. Email addresses:qianjianghhu@sina.com (J. Qian), zsj@hhu.edu.cn (S.-J. Zheng), wangfan@njau.edu.cn (F. Wang), paul212063@hhu.edu.cn (Z.-J. Fu)
*Corresponding author. Email addresses:qianjianghhu@sina.com (J. Qian), zsj@hhu.edu.cn (S.-J. Zheng), wangfan@njau.edu.cn (F. Wang), paul212063@hhu.edu.cn (Z.-J. Fu)
*Corresponding author. Email addresses:qianjianghhu@sina.com (J. Qian), zsj@hhu.edu.cn (S.-J. Zheng), wangfan@njau.edu.cn (F. Wang), paul212063@hhu.edu.cn (Z.-J. Fu)
*Corresponding author. Email addresses:qianjianghhu@sina.com (J. Qian), zsj@hhu.edu.cn (S.-J. Zheng), wangfan@njau.edu.cn (F. Wang), paul212063@hhu.edu.cn (Z.-J. Fu)
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Abstract

In this paper, bymeans of a new recursive algorithm of non-tensor-product-typed divided differences, bivariate polynomial interpolation schemes are constructed over nonrectangular meshes firstly, which is converted into the study of scattered data interpolation. And the schemes are different as the number of scattered data is odd and even, respectively. Secondly, the corresponding error estimation is worked out, and an equivalence is obtained between high-order non-tensor-product-typed divided differences and high-order partial derivatives in the case of odd and even interpolating nodes, respectively. Thirdly, several numerical examples illustrate the recursive algorithms valid for the non-tensor-product-typed interpolating polynomials, and disclose that these polynomials change as the order of the interpolating nodes, although the node collection is invariant. Finally, from the aspect of computational complexity, the operation count with the bivariate polynomials presented is smaller than that with radial basis functions.

Keywords

Bivariate polynomial interpolationNonrectangular meshesScattered data interpolationThe conformality of smoothing cofactor methodRadial basis function

MSC classification

Secondary: 65D05: Interpolation
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 4 , November 2016 , pp. 549 - 578
Copyright
Copyright © Global-Science Press 2016 

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