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Mat. Zametki, 2005, Volume 78, Issue 1, Pages 98–114 (Mi mz2565)  

This article is cited in 1 scientific paper (total in 1 paper)

On the Orders of Nonlinear Approximations for Classes of Functions of Given Form

V. N. Konovalov

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: Suppose that $\Delta^s_+$ is the set of functions $x\colon I\to\mathbb R$ on a finite interval $I$ such that the divided differences $[x;t_0,…,t_s]$ of order $s\in\mathbb N$ of these functions are nonnegative for all collections from $(s+1)$ different points $t_0,…,t_s\in I$. For all $s\in\mathbb N$ and $1\le p\le\infty$, we establish exact orders of best approximations by splines with free nodes and rational functions in the metrics of $L_p$ for classes $\Delta^s_+B_p:=\Delta^s_+\cap B_p$, where $B_p$ is the unit ball in $L_p$. We also establish the asymptotics of pseudodimensional widths in $L_p$ of these classes of functions.

DOI: https://doi.org/10.4213/mzm2565

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English version:
Mathematical Notes, 2005, 78:1, 88–104

Bibliographic databases:

UDC: 517.5
Received: 28.06.2004

Citation: V. N. Konovalov, “On the Orders of Nonlinear Approximations for Classes of Functions of Given Form”, Mat. Zametki, 78:1 (2005), 98–114; Math. Notes, 78:1 (2005), 88–104

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. N. Konovalov, V. E. Maiorov, “Widths of some classes of convex functions and bodies”, Izv. Math., 74:1 (2010), 127–150  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математические заметки Mathematical Notes
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