Results 11 to 20 of about 16,329 (217)

Rectangular Vandermonde matrices on Chebyshev nodes

Linear Algebra and its Applications, 2001
A rectangular Vandermonde matrix \(V=\{V_{ij}\}= \{x_i^{j-1}\}\) \((i=1,\dots, n;\;j=1,\dots, m;\;n\leq m)\) defined on the so-called Chebyshev nodes (the roots of Chebyshev polynomials of the first order) is studied, by making use of combinatorial identities from number theory [cf. \textit{A. Eisinberg}, \textit{P. Pugliese}, and \textit{N.
A. Eisinberg, Giuseppe Franzè, N. Salerno   +2 more
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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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A polynomial interpolation process at quasi-Chebyshev nodes with the FFT [PDF]

Mathematics of Computation, 2011
Interpolation polynomial p n p_n at the Chebyshev nodes cos ⁡ π j / n \cos \pi j/n ( 0 ≤ j ≤ n 0\le j\le n ) for smooth functions is known to converge fast as n →
Hiroshi Sugiura, Takemitsu Hasegawa
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Stability Analysis of Grünwald Interpolation Operators on Chebyshev Nodes [PDF]

In 1941, G. Grünwald proved the convergence of a sequence of operators constructed using classical Lagrange interpolation at Chebyshev nodes. In this work, we establish a perturbed version of Grünwald's result, thereby extending the class of admissible nodal points.
P C Vinaya
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On Hermite-Fejér type interpolation on the Chebyshev nodes [PDF]

Bulletin of the Australian Mathematical Society, 1993
Given f ∈ C [−1, 1], let Hn, 3(f, x) denote the (0,1,2) Hermite-Fejér interpolation polynomial of f based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |Hn, 3(f, x) − f(x)|. Further, we demonstrate a method of combining the divergent Lagrange and (0,1,2) interpolation methods on the ...
Graeme Byrne, T. M. Mills, Simon J. Smith   +2 more
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Lebesgue constants for polyhedral sets and polynomial interpolation on\n Lissajous-Chebyshev nodes [PDF]

Journal of Complexity, 2016
29 pages, 1 ...
Peter Dencker, Wolfgang Erb, Yurii Kolomoitsev, Tetiana Lomako   +3 more
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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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Electrocardiogram reconstruction based on Hermite interpolating polynomial with Chebyshev nodes

Indonesian Journal of Electrical Engineering and Computer Science
Electrocardiogram (ECG) signals generate massive volume of digital data, so they need to be suitably compressed for efficient transmission and storage. Polynomial approximations and polynomial interpolation have been used for ECG data compression where the data signal is described by polynomial coefficients only.
Shashwati Ray, Vandana Chouhan
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Estimating the Lebesgue constant for the Chebyshev distribution of nodes

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2023
In this paper an approach to estimation of the Lebesgue constant for the Lagrange interpolation process with nodes in the zeros of Chebyshev polynomials of the first kind is done. Two-sided estimation of this constant is carried out by using the logarithmic derivative of the Euler gamma function and of the Riemann zeta function.
Oksana V. Germider, В. Н. Попов
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Alternating polynomials associated with the Chebyshev extrema nodes

Journal of Approximation Theory, 1988
For a given set \(X=\{x_ k\}_ 0^{n+1}\) of nodes in [-1,1], the author introduces an operator \(A_ n(X;x)\) mapping functions in C[-1,1] into polynomials of degree n. They were called `generalized alternating polynomials'. Here X is specialized to \(U=\{\cos k\pi /n+1\}_ 0^{n+1}\), the extrema of Chebyshev polynomials of the first kind.
L. Brutman
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