Results 1 to 10 of about 935 (177)

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
doaj   +3 more sources

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, Len Bos
exaly   +3 more sources

Efficient Non-Interactive Discrete ReLU over CKKS Using Interpolation Look-Up Table [PDF]

Entropy
Deploying neural networks on encrypted data requires efficient evaluation of nonlinear activations, especially the ReLU function, without decryption.
Zhigang Chen, Xinxia Song, Liqun Chen
doaj   +2 more sources

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
doaj   +5 more sources

Trigonometric Sums via Lagrange Interpolation

Axioms
By means of the Lagrange interpolation, we derive two trigonometric identities that are utilized to evaluate, in closed forms, eight classes of power sums of trigonometric functions over equally distributed angles around the unit circle.
Marta Na Chen, Wenchang Chu, Xiaoyuan Wang   +2 more
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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 Juhasz, Agoston Roth
exaly   +3 more sources

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source