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@article{PA_2017_6_2_a0, author = {G. G. Akniyev}, title = {Discrete least squares approximation of piecewise-linear functions by trigonometric polynomials}, journal = {Problemy analiza}, pages = {3--24}, publisher = {mathdoc}, volume = {6}, number = {2}, year = {2017}, language = {en}, url = {http://geodesic.mathdoc.fr/item/PA_2017_6_2_a0/} }
G. G. Akniyev. Discrete least squares approximation of piecewise-linear functions by trigonometric polynomials. Problemy analiza, Tome 6 (2017) no. 2, pp. 3-24. http://geodesic.mathdoc.fr/item/PA_2017_6_2_a0/
[1] Bernshtein S. N., “On trigonometric interpolation by the method of least squares”, Dokl. Akad. Nauk USSR, 4 (1934), 1–5 (in Russian)
[2] Courant R., Differential and Integral Calculus, v. 1, Wiley-Interscience, New Jersey, 1988, 704 pp. | MR
[3] Erdös P., “Some theorems and remarks on interpolation”, Acta Sci. Math. (Szeged), 12 (1950), 11–17 | MR | Zbl
[4] Fikhtengol'ts G. M., Course of differential and integral calculus, v. 1, Fizmatlit, M., 1969, 656 pp. (in Russian)
[5] Kalashnikov M. D., “On polynomials of best (quadratic) approximation on a given system of points”, Dokl. Akad. Nauk USSR, 105 (1955), 634–636 (in Russian) | MR
[6] Krilov V. I., “Convergence of algebraic interpolation with respect to the roots of a Chebyshev polynomial for absolutely continuous functions and functions with bounded variation”, Dokl. Akad. Nauk USSR, 107 (1956), 362–365 (in Russian) | MR
[7] Magomed-Kasumov M. G., “Approximation properties of de la Valle-Poussin means for piecewise smooth functions”, Mat. Zametki, 100:2 (2016), 229–244 | DOI | MR | Zbl
[8] Marcinkiewicz J., “Quelques remarques sur l'interpolation”, Acta Sci. Math. (Szeged), 8 (1936), 127–130 (in French)
[9] Marcinkiewicz J., “Sur la divergence des polynômes d'interpolation”, Acta Sci. Math. (Szeged), 8 (1936), 131–135 (in French)
[10] Natanson I. P., “On the Convergence of Trigonometrical Interpolation at Equi-Distant Knots”, Annals of Mathematics, Second Series, 45:3 (1944), 457–471 | DOI | MR | Zbl
[11] Nikol'skii S. M., “On some methods of approximation by trigonometric sums”, Mathematics of the USSR–Izvestiya, 4 (1940), 509–520 (in Russian)
[12] Šarapudinov I. I., “On the best approximation and polynomials of the least quadratic deviation”, Anal. Math., 9:3, 223–234 | MR
[13] Zygmund A., Trigonometric Series, v. 1, Cambridge University Press, Cambridge, 1959, 747 pp. | MR | Zbl