A recursive algorithm for Hermite interpolation over a triangular grid
Journal of Computational and Applied Mathematics - Special issue on scattered data
On Bivariate Hermite Interpolation with Minimal Degree Polynomials
SIAM Journal on Numerical Analysis
On the history of multivariate polynomial interpolation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 vol. II: interpolation and extrapolation
Multivariate Hermite interpolation by algebraic polynomials: a survey
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 vol. II: interpolation and extrapolation
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
The proper interpolation space for multivariate Birkhoff interpolation
Journal of Computational and Applied Mathematics
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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=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; 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.