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Cubic Trigonometric Hermite Interpolation Curve: Construction, Properties, and Shape Optimization
Journal of Function Spaces, 2022 Cubic Hermite interpolation curve plays a very important role in interpolation curves modeling, but it has three shortcomings including low continuity, difficult shape adjustment, and the inability to accurately represent some common engineering curves ...
Juncheng Li, Chengzhi Liu
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On the degree of approximation of the Hermite and Hermite-Fejer interpolation [PDF]
International Journal of Mathematics and Mathematical Sciences, 1992 Here we find the order of convergence of the Hermite and Hermite-Fejér interpolation polynomials constructed on the zeros of (1−x2)Pn(x) where Pn(x) is the Legendre polynomial of degree n with normalization Pn(1)=1.
J. Prasad
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ON HERMITE INTERPOLATION AND DIVIDED DIFFERENCES [PDF]
Surveys in Mathematics and its Applications, 2020 This paper is a survey of topics related to Hermite interpolation. In the first part we present the standard analysis of the Hermite interpolation problem. Existence, uniqueness and error formula are included.
François Dubeau
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On the singularity of multivariate Hermite interpolation
Journal of Computational and Applied Mathematics, 2014 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 $d\geq 2k$. And then we solve the
Zhaoliang Meng, Zhongxuan Luo
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Curve and Surface Construction Using Hermite Trigonometric Interpolant
Mathematical and Computational Applications, 2021 In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using the derivatives are presented. The combination of tension, continuity, and bias control is used as a very powerful type of interpolation; they
Fatima Oumellal, Abdellah Lamnii
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Barycentric Hermite Interpolation [PDF]
SIAM Journal on Scientific Computing, 2013 Let $z_{1},\ldots,z_{K}$ be distinct grid points. If $f_{k,0}$ is the prescribed value of a function at the grid point $z_{k}$, and $f_{k,r}$ the prescribed value of the $r$\foreignlanguage{american}{-th} derivative, for $1\leq r\leq n_{k}-1$, the Hermite interpolant is the unique polynomial of degree $N-1$ ($N=n_{1}+\cdots+n_{K}$) which interpolates ...
Burhan A. Sadiq, Divakar Viswanath
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Mathematics, 2023 In this paper, we focus on the numerical solution of the second kind of Volterra integral equation with a highly oscillatory Fourier kernel. Based on the calculation of the modified moments, we propose four collocation methods to solve the equations ...
Jianyu Wang, Chunhua Fang, Guifeng Zhang
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A note on optimal Hermite interpolation in Sobolev spaces
Journal of Inequalities and Applications, 2022 This paper investigates the optimal Hermite interpolation of Sobolev spaces W ∞ n [ a , b ] $W_{\infty }^{n}[a,b]$ , n ∈ N $n\in \mathbb{N}$ in space L ∞ [ a , b ] $L_{\infty }[a,b]$ and weighted spaces L p , ω [ a , b ] $L_{p,\omega }[a,b]$ , 1 ≤ p < ∞ $
Guiqiao Xu, Xiaochen Yu
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The EH Interpolation Spline and Its Approximation
Abstract and Applied Analysis, 2014 A new interpolation spline with two parameters, called EH interpolation spline, is presented in this paper, which is the extension of the standard cubic Hermite interpolation spline, and inherits the same properties of the standard cubic Hermite ...
Jin Xie, Xiaoyan Liu
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Applied Sciences, 2021 As for industrial robots’ point-to-point joint motion planning with constrained velocity, cubic polynomial planning has the problem of discontinuous acceleration; quintic polynomial planning requires acceleration to be specified in advance, which will ...
Yasong Pu +4 more
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