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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 7515876, 11 pages
http://dx.doi.org/10.1155/2016/7515876
Research Article

On the Singularity of Multivariate Hermite Interpolation of Total Degree

1School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2School of Mathematics and Statistics, Taishan College, Taian 271021, China
3School of Software, Dalian University of Technology, Dalian 116620, China

Received 4 March 2016; Accepted 2 August 2016

Academic Editor: Guang Zhang

Copyright © 2016 Zhongyong Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the singularity of multivariate Hermite interpolation of type total degree on nodes with . We first check the number of the interpolation conditions and the dimension of interpolation space. And then the singularity of the interpolation schemes is decided for most cases. Also some regular interpolation schemes are derived, a few of which are proved due to theoretical argument and most of which are verified by numerical method. There are some schemes to be decided and left open.