Standing waves in the first order spline-wavelet decomposition

2013 ◽  
Vol 5 (4) ◽  
pp. 404-408 ◽  
Author(s):  
Yu. K. Dem’yanovich
Keyword(s):  
Wavelet Decomposition ◽  
Standing Waves ◽  
Spline Wavelet ◽  
First Order ◽  
Order Spline

Realization of the Spline-Wavelet Decomposition of the First Order

2017 ◽  
Vol 224 (6) ◽  
pp. 833-860 ◽  
Author(s):  
Yu. K. Dem’yanovich ◽  
A. S. Ponomarev
Keyword(s):  
Wavelet Decomposition ◽  
Spline Wavelet ◽  
First Order

scholarly journals On Wavelet Decomposition of the Singular Splines

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Wavelet Decomposition ◽  
Spline Wavelet ◽  
The Creation ◽  
Embedded Grids

One of the approaches to the problem of approximating functions with a singularity is the creation of an approximating apparatus based on splines with the same feature. For the wavelet decomposition of spline spaces it is important that the property of the embedding of these spaces is associated with embedding grids. The purpose of this paper is to consider ways of constructing spaces of splines with a predefined singularity and obtain their wavelet decomposition. Here the concept of generalized smoothness is used, within which the mentioned singularity is generalized smooth. This approach leads to the construction of a system of embedded spaces on embedded grids. A spline-wavelet decomposition of mentioned spaces is presented. Reconstruction formulas are done

Integer Realization of Spline-Wavelet Decomposition

2017 ◽  
Vol 228 (6) ◽  
pp. 639-654
Author(s):  
Yu. K. Dem’yanovich ◽  
O. N. Ivantsova ◽  
A. Yu. Ponomareva
Keyword(s):  
Wavelet Decomposition ◽  
Spline Wavelet

scholarly journals Spaces of polynomial and nonpolynomial spline-wavelets

2019 ◽  
Vol 292 ◽  
pp. 04001
Author(s):  
Yu. K. Dem’yanovich ◽  
I. G. Burova ◽  
T. O. Evdokimovas ◽  
A. V. Lebedeva
Keyword(s):  
Interpolation Problem ◽  
Wavelet Decomposition ◽  
Hermite Interpolation ◽  
Uniform Grid ◽  
First Order ◽  
Spline Wavelets ◽  
Almost Everywhere

This paper, discusses spaces of polynomial and nonpolynomial splines suitable for solving the Hermite interpolation problem (with first-order derivatives) and for constructing a wavelet decomposition. Such splines we call Hermitian type splines of the first level. The basis of these splines is obtained from the approximation relations under the condition connected with the minimum of multiplicity of covering every point of (α, β) (almost everywhere) with the support of the basis splines. Thus these splines belong to the class of minimal splines. Here we consider the processing of flows that include a stream of values of the derivative of an approximated function which is very important for good approximation. Also we construct a splash decomposition of the Hermitian type splines on a non-uniform grid.

scholarly journals On approximation of two-dimensional potential and singular operators

2019 ◽  
Vol 2019 (1) ◽  
pp. 68-83
Author(s):  
Charyyar Ashyralyyev ◽  
Sedanur Efe
Keyword(s):  
Numerical Calculation ◽  
Singular Integral ◽  
Numerical Experiments ◽  
Spline Approximation ◽  
Integral Operators ◽  
Quadrature Formulas ◽  
Two Dimensional ◽  
Order Of Accuracy ◽  
First Order ◽  
Order Spline

Abstract The purpose of this paper is the construction of second-order of accuracy quadrature formulas for the numerical calculation of the Vekua types two-dimensional potential and singular integral operators in the unit disk of complex plane. We propose quadrature formulas for these integrals which based on first-order spline approximation of two-dimensional function. MATLAB programs are used for numerical experiments in test examples.

Structure of two–nested spline–wavelet decomposition

2013 ◽  
Vol 189 (3) ◽  
pp. 388-401
Author(s):  
Yu. K. Dem’yanovich ◽  
V. O. Dron’
Keyword(s):  
Wavelet Decomposition ◽  
Spline Wavelet
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