Results 1 to 10 of about 1,315 (192)
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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Mathematical Modelling and Analysis, 1999 One of the simplest schemes of the degenerate matrix method with nodes as zeroes of Chebyshev polynomials of the second kind is considered. Performance of simple iterations and some modifications of Newton method for the discrete problem is compared ...
T. Cirulis, O. Lietuvietis
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Vandermonde matrices with Chebyshev nodes [PDF]
Linear Algebra and its Applications, 2007 AbstractFor an N×N Vandermonde matrix VN=(αji-1)1⩽ij⩽N with translated Chebyshev zero nodes, it is discovered that VNT admits an explicit QR decomposition with the R-factor consisting of the coefficients of the translated Chebyshev polynomials. This decomposition then leads to an exact expression for the Frobenius condition number of its submatrix Vk,N=
Ren‐Cang Li
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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.
Peter Dencker, Wolfgang Erb
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On the filtered polynomial interpolation at Chebyshev nodes [PDF]
Applied Numerical Mathematics, 2021 20 pages, 19 figures given in 8 eps ...
Donatella Occorsio, Woula Themistoclakis
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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 +2 more
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On Rational Interpolation to |x| at the Adjusted Chebyshev Nodes
Journal of Approximation Theory, 1998 The adjusted Chebyshev nodes on the interval \([0,1]\) are defined to be \[ \sin^2((2k-1)\pi/ 4n),\quad k= 1,2,\dots, n. \] Using that \(| x|\) is an even function, the study of its rational approximation on the interval \([-1,1]\) can be reduced to \([0,1]\).
L. Brutman
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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 +2 more
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Quadratures with multiple nodes for Fourier–Chebyshev coefficients [PDF]
IMA Journal of Numerical Analysis, 2017 Gaussian quadrature formulas, relative to the Chebyshev weight functions, with multiple nodes and their optimal extensions for computing the Fourier coefficients in expansions of functions with respect to a given system of orthogonal polynomials, are considered. The existence and uniqueness of such quadratures is proved. One of them is a generalization
Gradimir V. Milovanović +2 more
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Some remarks on filtered polynomial interpolation at Chebyshev nodes
, 2021 The present paper concerns filtered de la Vall e Poussin (VP) interpolation at the Chebyshev nodes of the four kinds. This approximation model is interesting for applications because it combines the advantages of the classical Lagrange polynomial approximation (interpolation and polynomial preserving) with the ones of filtered approximation (uniform ...
Donatella Occorsio, Woula Themistoclakis
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