On the Singularity of Multivariate Hermite Interpolation of Total Degree

Abstract

We study the singularity of multivariate Hermite interpolation of type total degree on m nodes with 3+d<m≤d(d+3)/2. 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.