On approximation by ridge functions

被引：21

作者：

Kroo, A

机构：

[1] Math. Inst. Hung. Acad. of Sci., Budapest

来源：

CONSTRUCTIVE APPROXIMATION | 1997年 / 13卷 / 04期

关键词：

ridge functions; homogeneous polynomials; fundamentality; rate of approximation;

D O I：

10.1007/s003659900053

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Ridge functions are defined as functions of the form f(a.x), where f:R --> R, x is an element of R-k, and a belongs to the given ''direction'' set A subset of R-k. In this paper we study the fundamentality of ridge functions for variable directions sets A and discuss the rate of approximation by ridge functions.

引用

页码：447 / 460

页数：14

共 8 条

[1]

Bernstein SN, 1952, COLLECTED WORKS, VI

[2] ON CERTAIN ORTHOGONAL POLYNOMIALS, NIKOLSKI-TYPE AND TURAN-TYPE INEQUALITIES, AND INTERPOLATORY PROPERTIES OF BEST APPROXIMANTS [J].