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Probl. Anal. Issues Anal., 2019, Volume 8(26), Issue 3, Pages 166–186 (Mi pa282)  

On the convergence of the least square method in case of non-uniform grids

M. S. Sultanakhmedov

Dagestan Scientific Center of RAS, 45, M.Gadzhieva st., Makhachkala, 367025, Russia

Abstract: Let $f(t)$ be a continuous on $[-1, 1]$ function, which values are given at the points of arbitrary non-uniform grid $\Omega_N= \{ t_j \}_{j=0}^{N-1}$, where nodes $t_j$ satisfy the only condition $\eta_{j}\leq t_{j}\leq\eta_{j+1},$ $0\leq j \leq N-1,$ and nodes $\eta_{j}$ are such that $-1=\eta_{0}<\eta_{1}<\eta_{2}<\cdots<\eta_{N-1}<\eta_{N}=1$. We investigate approximative properties of the finite Fourier series for $f(t)$ by algebraic polynomials $\hat{P}_{n, N}(t)$, that are orthogonal on $\Omega_N = \{ t_j \}_{j=0}^{N-1}$. Lebesgue-type inequalities for the partial Fourier sums by $\hat{P}_{n, N}(t)$ are obtained.

Keywords: random net, non-uniform grid, orthogonal polynomials, Legendre polynomials, least square method, Fourier series, function approximation.

DOI: https://doi.org/10.15393/j3.art.2019.6410

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Bibliographic databases:

UDC: 517.521
MSC: 42C10, 41A10, 33F05
Received: 03.06.2019
Revised: 22.10.2019
Accepted:18.10.2019
Language:

Citation: M. S. Sultanakhmedov, “On the convergence of the least square method in case of non-uniform grids”, Probl. Anal. Issues Anal., 8(26):3 (2019), 166–186

Citation in format AMSBIB
\Bibitem{Sul19}
\by M.~S.~Sultanakhmedov
\paper On the convergence of the least square method in case of non-uniform grids
\jour Probl. Anal. Issues Anal.
\yr 2019
\vol 8(26)
\issue 3
\pages 166--186
\mathnet{http://mi.mathnet.ru/pa282}
\crossref{https://doi.org/10.15393/j3.art.2019.6410}
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\elib{https://elibrary.ru/item.asp?id=41470790}


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