Results 1 to 10 of about 183 (122)
On the filtered polynomial interpolation at Chebyshev nodes [PDF]
Applied Numerical Mathematics, 2021 The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vallée Poussin filters. These polynomials can be an useful device for many theoretical and applicative problems since they combine the advantages of the classical Lagrange interpolation, with the uniform convergence
Donatella Occorsio +1 more
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Combined Shepard operators with Chebyshev nodes
Journal of Numerical Analysis and Approximation Theory, 2004 In this paper we study combined Shepard-Lagrange univariate interpolation operator\[S_{n,\mu}^{L,m}(Y;f,x):=S_{n,\mu}^{L,m}(f,x)=\frac{\sum\limits_{k=0}^{n+1}\left\vert x-y_{n,k}\right\vert ^{-\mu}(L_{m}f)(x,y_{n,k})}{\sum\limits_{k=0}^{n+1}\left\vert x ...
Cristina O. Oşan, Radu T. Trîmbitaş
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The Bernstein Constant and Polynomial Interpolation at the Chebyshev Nodes
Journal of Approximation Theory, 2002 By giving explicit upper bounds, the author shows that the Bernstein constants \[ B_{\lambda,p} := \lim_{n\to\infty} n^{\lambda+1/p} \inf_{c_k} \Biggl\| | x| ^\lambda - \sum^n_{k=0} c_k x^k\Biggl\|_{L_p[-1,1]} \] are finite for all \(\lambda > 0\) and \(p\in (1/3,\infty)\). For \(p = 1\), the upper bounds turn out to be sharp.
Michael I Ganzburg
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Multivariate polynomial interpolation on Lissajous–Chebyshev nodes
Journal of Approximation Theory, 2017 In this article, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets related to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes linked to these curves, we derive a discrete orthogonality structure on these node sets.
Wolfgang Erb
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On the asymptotics of polynomial interpolation to |x|α at the Chebyshev nodes
Journal of Approximation Theory, 2013 AbstractIn this paper, we discuss asymptotic relations for the approximation of |x|α,α>0 in L∞[−1,1] by Lagrange interpolation polynomials based on the zeros of the Chebyshev polynomials of first kind.
Michael Revers
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Lebesgue constants for polyhedral sets and polynomial interpolation on Lissajous–Chebyshev nodes
Journal of Complexity, 2017 29 pages, 1 ...
Yurii Kolomoitsev, Wolfgang Erb
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On Berman's phenomenon for (0,1,2) Hermite-Fejér interpolation
Journal of Numerical Analysis and Approximation Theory, 2019 Given \(f\in C[-1,1]\) and \(n\) points (nodes) in \([-1,1]\), the Hermite-Fejer interpolation (HFI) polynomial is the polynomial of degree at most \(2n-1\) which agrees with \(f\) and has zero derivative at each of the nodes. In 1916, L.
Graeme J Byrne, Simon Jeffrey Smith
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Efficient Authentication Scheme Based on Chebyshev Chaotic Map for VANET [PDF]
Jisuanji gongcheng, 2021 Vehicular Ad-hoc Network(VANET) plays an important role in the construction of intelligent transportation systems.The message authentication schemes can ensure the reliability and security of VANET in practical applications, but most of the existing ...
YANG Jiyun, YAO Ruidong, ZHOU Jie, GAO Lingyun
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Approximation by interpolation: the Chebyshev nodes [PDF]
Journal of Classical Analysis, 2020 Summary: In this paper, we first revisit the well-known result stating that the Hermite interpolation polynomials of a function \(f\) continuous on \([-1,1]\), with the zeros of the Chebyshev polynomials of the first kind as nodes, converge uniformly to \(f\) on \([-1,1]\).
Foupouagnigni, Mama +3 more
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Function correction and Lagrange – Jacobi type interpolation [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2023 It is well-known that the Lagrange interpolation based on the Chebyshev nodes may be divergent everywhere (for arbitrary nodes, almost everywhere), like the Fourier series of a summable function.
Novikov, Vladimir Vasil’evich
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