Results 1 to 10 of about 23,143 (202)
ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES [PDF]
Ural Mathematical Journal, 2017 The existence and uniqueness of an interpolating periodic spline defined on an equidistant mesh by the linear differential operator \({\cal L}_{2n+2}(D)=D^{2}(D^{2}+1^{2})(D^{2}+2^{2})\cdots (D^{2}+n^{2})\) with \(n\in\mathbb{N}\) are reproved under the ...
Sergey I. Novikov
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Subperiodic trigonometric interpolation and quadrature [PDF]
Applied Mathematics and Computation, 2012 The authors study subperiodic trigonometric interpolation and quadrature on \([-\omega, \omega]\) \((0 < \omega \leq \pi)\) at angular nodes \(\theta_j\) \((j=1,\ldots, 2n+1)\) which are the zeros of \(T_{2n+1}(\sin(\theta/2) / \sin(\omega/2))\). Here, \(T_{2n+1}\) denotes the \((2n+1)\)-th Chebyshev polynomial.
Marco Vianello
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On the arclength of trigonometric interpolants
Journal of Numerical Analysis and Approximation Theory, 2001 As pointed out recently by Strichartz [5], the arclength of the graph \(\Gamma(S_N(f))\) of the partial sums \(S_N(f)\) of the Fourier series of a jump function \(f\) grows with the order of \(\log N\).
Jürgen Prestin, Ewald Quak
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A scheme for interpolation with trigonometric spline curves
Journal of Computational and Applied Mathematics, 2014 In this paper the authors propose a method for interpolating trigonometric splines with class \(n>1\). The interpolants are calculated by blending two elliptical arcs with an appropriate trigonometric function. The proposed interpolation method is a generalization of the Overhauser spline.
Imre Juhász
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Some applications of Sigmoid functions [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2021 In numerical analysis, the process of fitting a function via given data is called interpolation. Interpolation has many applications in engineering and science.
M. A. Jafari, A. Aminataei
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An extension of Lagrange interpolation formula and its applications [PDF]
Mathematics and Computational Sciences, 2023 In this work, a new type of interpolation formula is introduced. These formulas can be an extension of the Lagrange interpolation formula. The error of this new type of interpolation is calculated. In order to display efficiency of the proposed formulas,
Mohammad Ali Jafari, Azim Aminataei
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Curve and Surface Construction Using Hermite Trigonometric Interpolant
Mathematical and Computational Applications, 2021 In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using the derivatives are presented. The combination of tension, continuity, and bias control is used as a very powerful type of interpolation; they
Fatima Oumellal, Abdellah Lamnii
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Cubic Trigonometric Hermite Interpolation Curve: Construction, Properties, and Shape Optimization
Journal of Function Spaces, 2022 Cubic Hermite interpolation curve plays a very important role in interpolation curves modeling, but it has three shortcomings including low continuity, difficult shape adjustment, and the inability to accurately represent some common engineering curves ...
Juncheng Li, Chengzhi Liu
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Generalized trigonometric interpolation [PDF]
Journal of Computational and Applied Mathematics, 2019 This article proposes a generalization of the Fourier interpolation formula, where a wider range of the basic trigonometric functions is considered. The extension of the procedure is done in two ways: adding an exponent to the maps involved, and considering a family of fractal functions that contains the standard case.
M. A. Navascués +3 more
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Construction of optimal interpolation formula exact for trigonometric functions by Sobolev’s method
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2022 The paper is devoted to derivation of the optimal interpolation formula in W2(0,2)(0,1) Hilbert space by Sobolev’s method. Here the interpolation formula consists of a linear combination ΣNβ=0Cβφ(xβ) of the given values of a function φ from the space ...
Shadimetov, Kh.M. +2 more
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