scholarly journals On the Singularity of Multivariate Hermite Interpolation of Total Degree

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Zhongyong Hu ◽  
Zhaoliang Meng ◽  
Zhongxuan Luo
Keyword(s):  
Numerical Method ◽  
Hermite Interpolation ◽  
Interpolation Space ◽  
Total Degree ◽  
Theoretical Argument ◽  
Multivariate Hermite Interpolation

We study the singularity of multivariate Hermite interpolation of type total degree onmnodes with3+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.

scholarly journals Cardinal Basis Piecewise Hermite Interpolation on Fuzzy Data

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
H. Vosoughi ◽  
S. Abbasbandy
Keyword(s):  
Numerical Method ◽  
Linear Space ◽  
Hermite Polynomial ◽  
Hermite Interpolation ◽  
Explicit Construction ◽  
Basis Functions ◽  
Full Detail ◽  
Extension Principle ◽  
Fuzzy Data ◽  
Case Based

A numerical method along with explicit construction to interpolation of fuzzy data through the extension principle results by widely used fuzzy-valued piecewise Hermite polynomial in general case based on the cardinal basis functions, which satisfy a vanishing property on the successive intervals, has been introduced here. We have provided a numerical method in full detail using the linear space notions for calculating the presented method. In order to illustrate the method in computational examples, we take recourse to three prime cases: linear, cubic, and quintic.

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