Results 21 to 30 of about 16,329 (217)
Rational interpolation with parameters based on Chebyshev nodes
FilomatA type of rational interpolation operator (RIO) with parameter ? is studied in this paper. We give the specific construction of RIO based on Chebyshev nodes of the fourth kind, and calculate the approximation order of the RIO to functions when 1 < ? < 2 and ? > 2 respectively. Furthermore, we analyze the relation between the parameter ?
Zheng Yan, Yi Zhao
openalex +3 more sources
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
openalex +2 more sources
The Lebesgue function for Lagrange interpolation on the augmented Chebyshev nodes
Publicationes Mathematicae Debrecen, 2005 Summary: Given \(f\in C[-1,1]\) and \(n\) points (nodes) in \([-1,1]\), the well-known Lagrange interpolation polynomial is the polynomial of minimum degree which agrees with \(f\) at each of the nodes. Properties of the Lebesgue function and Lebesgue constant associated with Lagrange interpolation on the Chebyshev nodes (the zeros of the \(n\)th ...
Simon J. Smith
openalex +2 more sources
Efficient Gaussian Process Calculations Using Chebyshev Nodes and Fast Fourier Transform [PDF]
ElectronicsGaussian processes have gained popularity in contemporary solutions for mathematical modeling problems, particularly in cases involving complex and challenging-to-model scenarios or instances with a general lack of data. Therefore, they often serve as generative models for data, for example, in classification problems.
Adrian Dudek, Jerzy Baranowski
openalex +2 more sources
The minimal number of nodes in Chebyshev type quadrature formulas
Indagationes Mathematicae, 1993 The authors abstract is accurate: We study Chebyshev type quadrature formulas of degree \(n\) with respect to a weight function on \(\langle - 1,+1 \rangle\), i.e. formulas \[ {1 \over {\int_{-1}^{+1} w(t)dt}}\cdot \int_{-1}^{+1} f(t) w(t) dt={1\over N} \sum_{i=1}^ N f(x_ i)+ R(f) \] with nodes \(x_ i\in \langle -1,+1\rangle\) such that \(R(f)=0\) for ...
Arno B. J. Kuijlaars
openalex +3 more sources
A numerical approach to fractional Volterra–Fredholm integro-differential problems using shifted Chebyshev spectral collocation [PDF]
Scientific ReportsThis study presents an innovative numerical framework for addressing initial value problems (IVPs) in linear fractional Volterra–Fredholm integro-differential equations (FVFIDEs).
Maha M. Hamood +2 more
doaj +2 more sources
Journal of Inequalities and Applications, 1999 For a fixed integer and , let denote the th fundamental polynomial for Hermite–Fejér interpolation on the Chebyshev nodes . (So is the unique polynomial of degree at most which satisfies , and whose first derivatives vanish at each ...
Smith Simon J
doaj +1 more source
306 The MCV scheme with Chebyshev node collocation
The Proceedings of The Computational Mechanics Conference, 2009 Feng Xiao, Satoshi Ii
openalex +2 more sources
Novel weak form quadrature element method with expanded Chebyshev nodes
Applied Mathematics Letters, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chunhua Jin, Xinwei Wang, Luyao Ge
openalex +2 more sources
On a Lebesgue constant of interpolation rational process at the Chebyshev – Markov nodes
Журнал Белорусского государственного университета: Математика, информатика, 2019 In the present paper estimate of a Lebesgue constant of the interpolation rational Lagrange process on the segment [−1 ,1] at the Chebyshev – Markov cosine fractions nodes is considered.
Yauheni A. Rouba +2 more
doaj +2 more sources