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Volume 19, Issue 2
Tetrahedral $C^m$ Interpolation by Rational Functions

Guo-Liang Xu, Chuan I Chu & Wei-Min Xue

J. Comp. Math., 19 (2001), pp. 131-138.

Published online: 2001-04

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  • Abstract

A general local $C^m (m \ge 0)$ tetrahedral interpolation scheme by polynomials of degree $4m+1$ plus low order rational functions from the given data is proposed. The scheme can have either $4m+1$ order algebraic precision if $C^{2m}$ data at vertices and $C^m$ data on faces are given or $k+E[k/3]+1$ order algebraic precision if $C^k (k \le 2m)$ data are given at vertices. The resulted interpolant and its partial derivatives of up to order $m$ are polynomials on the boundaries of the tetrahedra.

  • Keywords

$C^m$ interpolation, Rational functions, Tetrahedra.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-19-131, author = {Xu , Guo-LiangChu , Chuan I and Xue , Wei-Min}, title = {Tetrahedral $C^m$ Interpolation by Rational Functions}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {2}, pages = {131--138}, abstract = {

A general local $C^m (m \ge 0)$ tetrahedral interpolation scheme by polynomials of degree $4m+1$ plus low order rational functions from the given data is proposed. The scheme can have either $4m+1$ order algebraic precision if $C^{2m}$ data at vertices and $C^m$ data on faces are given or $k+E[k/3]+1$ order algebraic precision if $C^k (k \le 2m)$ data are given at vertices. The resulted interpolant and its partial derivatives of up to order $m$ are polynomials on the boundaries of the tetrahedra.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8964.html} }
TY - JOUR T1 - Tetrahedral $C^m$ Interpolation by Rational Functions AU - Xu , Guo-Liang AU - Chu , Chuan I AU - Xue , Wei-Min JO - Journal of Computational Mathematics VL - 2 SP - 131 EP - 138 PY - 2001 DA - 2001/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8964.html KW - $C^m$ interpolation, Rational functions, Tetrahedra. AB -

A general local $C^m (m \ge 0)$ tetrahedral interpolation scheme by polynomials of degree $4m+1$ plus low order rational functions from the given data is proposed. The scheme can have either $4m+1$ order algebraic precision if $C^{2m}$ data at vertices and $C^m$ data on faces are given or $k+E[k/3]+1$ order algebraic precision if $C^k (k \le 2m)$ data are given at vertices. The resulted interpolant and its partial derivatives of up to order $m$ are polynomials on the boundaries of the tetrahedra.

Guo-Liang Xu, Chuan I Chu & Wei-Min Xue. (2019). Tetrahedral $C^m$ Interpolation by Rational Functions. Journal of Computational Mathematics. 19 (2). 131-138. doi:
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