On the Singularity of Multivariate Hermite Interpolation

2013/01/29 by Meng, Zhaoliang, Luo, Zhongxuan
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1301.6857

Abstract

In this paper we study the singularity of multivariate Hermite interpolation of type total degree. We present a method to judge the singularity of the interpolation scheme considered and by the method 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≥ 2k. 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; for m=d+2 and m=d+3, only three cases and one case 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.

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