Results 11 to 20 of about 1,315 (192)

Multivariate Markov polynomial inequalities and Chebyshev nodes [PDF]

Journal of Mathematical Analysis and Applications, 2007
AbstractThis article considers the extension of V.A. Markov's theorem for polynomial derivatives to polynomials with unit bound on the closed unit ball of any real normed linear space. We show that this extension is equivalent to an inequality for certain directional derivatives of polynomials in two variables that have unit bound on the Chebyshev ...
Lawrence A. Harris
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A Lightweight Certificateless Authenticated Key Agreement Scheme Based on Chebyshev Polynomials for the Internet of Drones [PDF]

Sensors
The Internet of Drones (IoD) overcomes the physical limitations of traditional ground networks with its dynamic topology and 3D spatial flexibility, playing a crucial role in various fields.
Zhaobin Li, Zheng Ju, Hong Zhao, Zhanzhen Wei, Gongjian Lan   +4 more
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The Lebesgue function for generalized Hermite-Fejér interpolation on the Chebyshev nodes [PDF]

The ANZIAM Journal, 2000
AbstractThis paper presents a short survey of convergence results and properties of the Lebesgue function λm,n(x) for(0, 1, …, m)Hermite-Fejér interpolation based on the zeros of the nth Chebyshev polynomial of the first kind. The limiting behaviour as n → ∞ of the Lebesgue constant Λm,n = max{λm,n(x): −1 ≤ x ≤ 1} for even m is then studied, and new ...
Graeme Byrne, T. M. Mills, Simon J. Smith   +2 more
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The Lebesgue function for Hermite-Fejér interpolation on the extended Chebyshev nodes [PDF]

Bulletin of the Australian Mathematical Society, 2002
Given f ∈ C[−1, 1] and n point (nodes) in [−1, 1], the Hermite-Fejér interpolation polynomial is the polynomial of minimum degree which agrees with f and has zero derivative at each of the nodes. In 1916, L. Fejér showed that if the nodes are chosen to be zeros of Tn (x), the nth Chebyshev polynomial of the first kind, then the interpolation ...
Simon J. Smith
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Rational interpolation to |x| at the Chebyshev nodes [PDF]

Bulletin of the Australian Mathematical Society, 1997
Recently the authors considered Newman-type rational interpolation to |x| induced by arbitrary sets of interpolation nodes and showed that under mild restrictions on the location of the interpolation nodes, the corresponding sequence of rational interpolants converges to |x|.
L. Brutman, Eli Passow
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On Generalized Hermite–Fejér Interpolation of Lagrange Type on the Chebyshev Nodes

Journal of Approximation Theory, 2000
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Graeme Byrne, T. M. Mills, Simon J. Smith   +2 more
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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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Hermite-Fejer interpolation at the ‘practical’ Chebyshev nodes [PDF]

Bulletin of the Australian Mathematical Society, 1973
Berman has raised the question in his work of whether Hermite-Fejér interpolation based on the so-called “practical” Chebyshev points, , 0(1)n, is uniformly convergent for all continuous functions on the interval [−1, 1]. In spite of similar negative results by Berman and Szegö, this paper shows this result is true, which is in accord with the great ...
R. D. Riess
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Chebyshev interpolation with approximate nodes of unrestricted multiplicity

Journal of Approximation Theory, 1989
Etude de l'interpolation polynomiale d'ordre superieur des fonctions regulieres sur un intervalle fini. Etablissement d'une estimation asymptotique liant les proprietes de differentiabilite de la fonction interpolee a une condition sur la distribution asymptotique des nœuds qui elimine le phenomene de ...
Gilbert Stengle
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Approximation by Nonlinear Hermite-Fejer interpolation operators of max-product kind on Chebyshev nodes

Journal of Numerical Analysis and Approximation Theory, 2010
The aim of this note is that by using the so-called max-product method, to associate to the Hermite-Fejer polynomials based on the Chebyshev knots of first kind, a new interpolation operator for which a Jackson-type approximation order in terms of ...
Lucian Coroianu, Sorin G. Gal
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