TY - JOUR
T1 - Trivariate Polynomial Natural Spline for 3D Scattered Data Hermit Interpolation
AU - Xu , Yingxiang
AU - Guan , Lü-Tai
AU - Xu , Weizhi
JO - Communications in Mathematical Research 
VL - 2
SP - 159
EP - 172
PY - 2021
DA - 2021/05
SN - 28
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19059.html
KW - scattered data, Hermit interpolation, natural spline.
AB - <p style="text-align: justify;">Consider a kind of Hermit interpolation for scattered data of 3D by
trivariate polynomial natural spline, such that the objective energy functional (with
natural boundary conditions) is minimal. By the spline function methods in Hilbert
space and variational theory of splines, the characters of the interpolation solution and
how to construct it are studied. One can easily find that the interpolation solution is
a trivariate polynomial natural spline. Its expression is simple and the coefficients can
be decided by a linear system. Some numerical examples are presented to demonstrate
our methods.</p>