Details:
Title  On the singularity of multivariate Hermite interpolation  Author(s)  Zhongxuan Luo, Zhaoliang Meng  Type  Article in Journal  Abstract  Abstract In this paper, we study the singularity of multivariate Hermite interpolation of type total degree. We present two methods to judge the singularity of the interpolation schemes considered and by methods to be developed, we show that all Hermite interpolation of type total degree on m = d + k points in R d is singular if d ≥ 2 k . And then we solve the Hermite interpolation problem on m ≤ d + 3 nodes completely. Precisely, all Hermite interpolations of type total degree on m ≤ d + 1 points with d ≥ 2 are singular; only three cases for m = d + 2 and one case for m = d + 3 can produce regular Hermite interpolation schemes, respectively. Besides, we also present a method to compute the interpolation space for Hermite interpolation of type total degree.  Keywords  Hermite interpolation, Singularity, Interpolation space, Polynomial ideal  ISSN  03770427 
URL 
http://www.sciencedirect.com/science/article/pii/S037704271300602X 
Language  English  Journal  Journal of Computational and Applied Mathematics  Volume  261  Number  0  Pages  85  94  Year  2014  Edition  0  Translation 
No  Refereed 
No 
