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 - <p style="text-align: justify;">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.</p>