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Volume 28, Issue 2
Trivariate Polynomial Natural Spline for 3D Scattered Data Hermit Interpolation

Yingxiang Xu, Lü-Tai Guan & Weizhi Xu

Commun. Math. Res., 28 (2012), pp. 159-172.

Published online: 2021-05

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  • Abstract

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.

  • Keywords

scattered data, Hermit interpolation, natural spline.

  • AMS Subject Headings

41A15, 65D07, 65D17

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-28-159, author = {Xu , YingxiangGuan , Lü-Tai and Xu , Weizhi}, title = {Trivariate Polynomial Natural Spline for 3D Scattered Data Hermit Interpolation}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {28}, number = {2}, pages = {159--172}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19059.html} }
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 -

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.

Xu , YingxiangGuan , Lü-Tai and Xu , Weizhi. (2021). Trivariate Polynomial Natural Spline for 3D Scattered Data Hermit Interpolation. Communications in Mathematical Research . 28 (2). 159-172. doi:
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