ON THE CONVERGENCE OF THE LEAST SQUARE METHOD IN CASE OF NON-UNIFORM GRIDS
Let f(t) be a continuous on [−1, 1] function, which values are given at the points of arbitrary non-uniform grid ΩN = = {tj} N−1 j=0 , where nodes tj satisfy the only condition ηj 6tj 6ηj+1, 0 6 j 6 N − 1, and nodes ηj are such that −1 = η0 < η1 < η2 < < · · · < ηN−1 < ηN = 1...
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Format: | Article |
Language: | English |
Published: |
Petrozavodsk State University
2019-11-01
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Series: | Проблемы анализа |
Subjects: | |
Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=6410&lang=en |
Summary: | Let f(t) be a continuous on [−1, 1] function, which values are given at the points of arbitrary non-uniform grid ΩN =
= {tj}
N−1
j=0 , where nodes tj satisfy the only condition ηj 6tj 6ηj+1,
0 6 j 6 N − 1, and nodes ηj are such that −1 = η0 < η1 < η2 <
< · · · < ηN−1 < ηN = 1. We investigate approximative properties
of the finite Fourier series for f(t) by algebraic polynomials Pˆ
n, N (t),
that are orthogonal on ΩN = {tj}
N−1
j=0 . Lebesgue-type inequalities
for the partial Fourier sums by Pˆ
n, N (t) are obtained.
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ISSN: | 2306-3424 2306-3432 |