1 citations · 2 across the 15 of their papers we have counts for
15 papers
Finite Fourier series. The class of trigonometric splines
Volodymyr Denysiuk, Lydmila Rybachuk
Finite trigonometric Fourier series on a set of discrete equidistant points are considered. A finite system of orthogonal functions that have interpolation and certain differential…
Forms of representation of interpolation trigonometric splines
Volodymyr Denysiuk, Lyudmila Rybachuk
Three forms of representation of trigonometric interpolation splines are considered, in particular, the representation by the coefficients of the interpolation trigonometric polyno…
Generalization of Trigonometric B-splines and Kernels of Interpolating Trigonometric Splines with Riemann Convergence Multipliers
Volodymyr Denysiuk, Olena Hryshko
This paper explores the generalization of the method for extracting Riemann trigonometric B-splines and Riemann kernels of trigonometric interpolation splines of arbitrary order on…
B-splines and kernels of trigonometric interpolation splines
Volodymyr Denysiuk, Olena Hryshko
This article focuses on trigonometric Riemann B-splines and Riemann kernels of trigonometric interpolation splines of arbitrary order; it is shown that trigonometric interpolation…
About norms, semi-norms and variation of trigonometric splines
V. Denysiuk
The work examines norms in of fundamental trigonometric splines of odd and even degrees, which in some cases coincide with polynomial ones. Fundamental trigonometric splines for th…
About some aspects of function interpolation by trigonometric splines
Volodymyr Denysiuk, Olena Hryshko
Interpolation of classes of differentiated functions given on a finite interval by trigonometric splines using the phantom node method is considered. This method consists in supple…
Polynomial and trigonometric splines
V. Denysiuk
Classes of simple polynomial and simple trigonometric splines given by Fourier series are considered. It is shown that the class of simple trigonometric splines includes the class…
About one method of constructing Hermite trigonometric splines
V. P. Denysiuk
The method of constructing trigonometric Hermite splines, which interpolate the values of some periodic function and its derivatives in the nodes of a uniform grid, is considered.…
Approximation, regularization and smoothing of trigonometric splines
V. Denysiuk
The methods of approximation, regularization and smoothing of trigonometric interpolation splines are considered in the paper. It is shown that trigonometric splines can be conside…
About some properties of simple trigonometric splines
V. P. Denysiuk
The class the trigonometric interpolation splines depending on the parameter vectors, selected convergence factors and interpolation factors is considered. The main prope…
Fundamental trigonometric interpolation and approximating polynomials and splines
V. P. Denysiuk
The paper deals with two fundamental types of trigonometric polynomials and splines on uniform grids, which allow us to construct interpolation approximations that depend linearly…
About one method of construction of interpolation trigonometric splines
V. Denysiuk
The method of constructing spline classes in the form of trigonometric Fourier series whose coefficients have a certain decreasing order are considered. in turn, this decrement det…
About one method for constructing Hermite trigonometric polynomials
V. P. Denysiuk
The method of constructing Hermite trigonometric polynomials, which interpolate the values of a certain periodic function and its derivatives up to (including ) the -th ( ) order i…
The method of summation of divergent trigonometric series
Volodymyr Denysiuk
The generalized summation of divergent trigonometric series, namely by method of -factors is considered in this paper. It is proved that such summation of Fourier series…
Method of improvement of convergence Fourier series and interpoliation polynomials in orthogonal functions
Volodymyr Denysiuk
There is proposed a method for improving the convergence of Fourier series by function systems, orthogonal at the segment, the application of which allows for smooth functions to r…