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This article is cited in 5 scientific papers (total in 5 papers)
Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency 2
V. F. Babenkoab, N. V. Parfinovichb a Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
b Dnepropetrovsk National University
Abstract:
We obtain exact values of best $L_1$-approximations for the classes $W^rF$, $r\in\mathbb N$, of periodic functions whose $r$th derivative belongs to a given rearrangement-invariant set $F$ as well as for the classes $W^rH^\omega$ of periodic functions whose $r$th derivative has a given convex (up) majorant $\omega(t)$ of the modulus of continuity by subspaces of polynomial splines of order $m\ge r+1$ of deficiency 2 with nodes at the points $2k\pi/n$, $n\in\mathbb N$, $k\in\mathbb Z$. It is shown that these subspaces are extremal for the Kolmogorov widths of the corresponding function classes.
Keywords:
periodic function, best $L_1$-approximation, periodic function, polynomial spline of deficiency 2, Kolmogorov width, rearrangement-invariant set, modulus of continuity.
Received: 07.03.2008
Citation:
V. F. Babenko, N. V. Parfinovich, “Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency 2”, Mat. Zametki, 85:4 (2009), 538–551; Math. Notes, 85:4 (2009), 515–527
Linking options:
https://www.mathnet.ru/eng/mzm4617https://doi.org/10.4213/mzm4617 https://www.mathnet.ru/eng/mzm/v85/i4/p538
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Abstract page: | 512 | Full-text PDF : | 211 | References: | 50 | First page: | 14 |
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