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On Approximation by Ridge Functions
被引:0
|作者:
A. Kroó
机构:
[1] Mathematical Institute of the Hungarian Academy of Sciences,
来源:
关键词:
Key words and phrases: Ridge functions, Homogeneous polynomials, Fundamentality, Rate of approximation. AMS Classification: 41A45, 41A63.;
D O I:
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学科分类号:
摘要:
Ridge functions are defined as functions of the form \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$f(\mbox{\footnotesize\bf a}\cdot \mbox{\footnotesize\bf x})$ \end{document} , where \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$f\colon\ {\Bbb R}\rightarrow {\Bbb R}$ \end{document} , \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$\mbox{\footnotesize\bf x}\in {\Bbb R}^k$, and $\mbox{\footnotesize\bf a}$ \end{document} belongs to the given ``direction'' set \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$A\subset {\Bbb R}^k$ \end{document} . In this paper we study the fundamentality of ridge functions for variable directions sets A and discuss the rate of approximation by ridge functions.
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页码:447 / 460
页数:13
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