arXiv subjects

S. S. Babaev

Publications and source records attributed to S. S. Babaev.

3 recordsLinked to original sources

arXiv2021

Optimal quadrature formulas for computing of Fourier integrals in a Hilbert space

In the present paper the optimal quadrature formulas in the sense of Sard are constructed for numerical integration of the integral $\int_a^b e^{2πiωx}φ(x)d x$ with $ω\in \mathbb{R}$ in the Hilbert space $W_2^{(2,1)}[a,b]$ of complex-valued functions. Furthermore, the explicit expressions for coefficients of the constructed optimal quadrature formulas are obtained. At the end of the paper some numerical results are presented.

math.NA↗

arXiv2020

On an optimal interpolation formula in $K_2(P_2)$ space

The paper is devoted to the construction of an optimal interpolation formula in $K_2(P_2)$ Hilbert space. Here the interpolation formula consists of a linear combination $\sum_{β=0}^NC_β(z)φ(x_β)$ of given values of a function $φ$ from the space $K_2(P_2)$. The difference between functions and the interpolation formula is considered as a linear functional called the error functional. The error of the interpolation formula is estimated by the norm of the error functional. We obtain the optimal interpolation formula by minimizing the norm of the error functional by coefficients $C_β(z)$ of the interpolation formula. The obtained optimal interpolation formula is exact for trigonometric functions $\sinωx$ and $\cosωx$. At the end of the paper, we give some numerical results which confirm our theoretical results.

math.NA↗

arXiv2018

Optimal interpolation formulas in $W_2^{(m,m-1)}$ space

In the present paper optimal interpolation formulas are constructed in $W_2^{(m,m-1)}(0,1)$ space. Explicit formulas for coefficients of optimal interpolation formulas are obtained. Some numerical results are presented.

math.NA↗