scholarly journals Calculating Methods for the Irregular Hermite Interpolation Polynomial

2013 ◽  
Author(s):  
Miao Luo ◽  
Liangliang Ma
Keyword(s):  
Hermite Interpolation ◽  
Interpolation Polynomial ◽  
Hermite Interpolation Polynomial

Calculating Methods for the Irregular Hermite Interpolation Polynomial

2013 ◽  
Vol 765-767 ◽  
pp. 620-624
Author(s):  
Miao Luo ◽  
Liang Liang Ma
Keyword(s):  
Hermite Interpolation ◽  
Interpolation Polynomial ◽  
Basic Function ◽  
Difference Quotients ◽  
Hermite Interpolation Polynomial ◽  
Multiple Difference

Based on the theory of the regular Hermite interpolation polynomial, several calculating methods including basic function, multiple difference quotients, etc., have been proposed to solve the complex irregular Hermite interpolation polynomial.

scholarly journals Full Hermite interpolation of the reliability of a hammock network

2020 ◽  
Vol 14 (1) ◽  
pp. 198-220 ◽  
Author(s):  
Leonard Dăuş ◽  
Marilena Jianu
Keyword(s):  
General Formula ◽  
Hermite Interpolation ◽  
Interpolation Polynomial ◽  
Arbitrary Size ◽  
Reliability Polynomial ◽  
Combinatorial Formulas ◽  
Hermite Interpolation Polynomial

Although the hammock networks were introduced more than sixty years ago, there is no general formula of the associated reliability polynomial. Using the full Hermite interpolation polynomial, we propose an approximation for the reliability polynomial of a hammock network of arbitrary size. In the second part of the paper, we provide combinatorial formulas for the first two non-zero coefficients of the reliability polynomial.

scholarly journals Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Renzhong Feng ◽  
Yanan Zhang
Keyword(s):  
Interior Point ◽  
Hermite Interpolation ◽  
High Efficiency ◽  
Scattered Data ◽  
Interpolation Polynomial ◽  
Computational Point ◽  
Large Sets ◽  
Approximate Derivative ◽  
Hermite Interpolation Polynomial ◽  
Hermite Interpolations

The requirements for interpolation of scattered data are high accuracy and high efficiency. In this paper, a piecewise bivariate Hermite interpolant satisfying these requirements is proposed. We firstly construct a triangulation mesh using the given scattered point set. Based on this mesh, the computational point (x,y) is divided into two types: interior point and exterior point. The value of Hermite interpolation polynomial on a triangle will be used as the approximate value if point (x,y) is an interior point, while the value of a Hermite interpolation function with the form of weighted combination will be used if it is an exterior point. Hermite interpolation needs the first-order derivatives of the interpolated function which is not directly given in scatted data, so this paper also gives the approximate derivative at every scatted point using local radial basis function interpolation. And numerical tests indicate that the proposed piecewise bivariate Hermite interpolations are economic and have good approximation capacity.

scholarly journals APPLICATION OF FUNCTIONAL RELATIONS TO MODELING BY MEANS OF DIFFERENTIAL EQUATIONS

2020 ◽  
pp. 454-458
Author(s):  
E. Kenenbaev ◽  
Dzh. A. Akerova ◽  
L. Askar kyzy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hermite Interpolation ◽  
Interpolation Polynomial ◽  
Mean Value ◽  
Elliptic Type ◽  
Partial Differential ◽  
Functional Relations ◽  
Finite Set ◽  
Hermite Interpolation Polynomial

Modeling by means of differential equations is considered in the paper. Their solutions are constructed on the base of functional relations connecting values of a solution of the equation in different points (infinite or finite set of values). For examples, even, odd and periodical solutions, Vallée-Poussin’s assertion, Lagrange interpolation polynomial, Hermite interpolation polynomial, spline-functions for ordinary differential equations, Asgeirsson’s identity and its generalizations for partial differential equations of hyperbolic type, “mean value” for partial differential equations of elliptic type are considered. Also, if an equation is close to one of considered types then an assertion is to be fulfilled approximately. Some estimations are found for such examples. An application of such relations to investigate some problems of interpolation and extrapolation is demonstrated.

Research on Smooth Support Vector Regression Based on Hermite

2011 ◽  
Vol 255-260 ◽  
pp. 2215-2219
Author(s):  
Bin Ren ◽  
Liang Lun Cheng
Keyword(s):  
Support Vector Regression ◽  
Hermite Interpolation ◽  
Interpolation Polynomial ◽  
Support Vector ◽  
Polynomial Functions ◽  
Smooth Approximation ◽  
Approximation Accuracy ◽  
Support Vector Regression Model ◽  
Hermite Interpolation Polynomial ◽  
Interpolation Functions

Polynomial smooth techniques are applied to Support Vector Regression model by an accurate smooth approximation which is offered by Hermite Interpolation polynomial. We use Hermite Interpolation to generate a new polynomial smooth function which is proposed for thefunction in ε-insensitive support vector regression of interpolation functions. Their important property is discussed. It can be shown that the approximation accuracy and smoothing rank of polynomial functions can be as high as required.

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