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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 03.06.2019 Revised: 22.10.2019 Accepted: 18.10.2019
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
Linking options:
https://www.mathnet.ru/eng/pa282 https://www.mathnet.ru/eng/pa/v26/i3/p166
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