A note on the criterion for a best approximation by superpositions of functions

被引：0

作者：

Ismailov, Vugar E. ^{[1
]}

机构：

[1] NAS Azerbaijan, Inst Math & Mech, AZ-1141 Baku, Azerbaijan

来源：

STUDIA MATHEMATICA | 2018年 / 240卷 / 02期

关键词：

Chebyshev alternation theorem; best approximation; path; weak*convergence; Banach-Alaoglutheorem; REPRESENTATION; INTERPOLATION;

D O I：

10.4064/sm170314-9-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Q be a compact subset of the d-dimensional Euclidean space, and C(Q) be the space of continuous real-valued functions on Q. We consider the problem of approximation of a function f is an element of C(Q) by superpositions of the form g o s + h o p, where s, p are fixed functions from C(Q) and g, h are variable univariate functions. We obtain a Chebyshev-type criterion for a function g0 o s + h0 o p to be a best approximation to f.

引用

页码：193 / 199

页数：7

共 25 条

[11] Interpolation on lines by ridge functions
Ismailov, V. E.
Pinkus, A.
[J]. JOURNAL OF APPROXIMATION THEORY, 2013, 175 : 91 - 113
[12] Ismailov V. E., 2006, INT J MATH MATH SCI
[13] On the representation by linear superpositions
Ismailov, Vugar E.
[J]. JOURNAL OF APPROXIMATION THEORY, 2008, 151 (02) : 113 - 125
[14] On the approximation by compositions of fixed multivariate functions with univariate functions
Ismailov, Vugar E.
[J]. STUDIA MATHEMATICA, 2007, 183 (02) : 117 - 126
[15] Approximation by ridge functions and neural networks with a bounded number of neurons
Ismailov, Vugar E.
[J]. APPLICABLE ANALYSIS, 2015, 94 (11) : 2245 - 2260
[16] A note on the representation of continuous functions by linear superpositions
Ismailov, Vugar E.
[J]. EXPOSITIONES MATHEMATICAE, 2012, 30 (01) : 96 - 101
[17] Khavinson S. Ya., 1969, MATH USSR IZV, V33, p[650, 617]
[18] When is f(x1,x2, ... ,xn) = u1(x1)+u2(x2)+•••+un(xn)?
Klopotowski, A
Nadkarni, MG
Rao, KPSB
[J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2003, 113 (01): : 77 - 86
[19] Klopotowski A, 2000, C MATH, V84, P385
[20] APPROXIMATION BY A SUM OF 2 ALGEBRAS - THE LIGHTNING BOLT PRINCIPLE
MARSHALL, DE
OFARRELL, AG
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1983, 52 (03) : 353 - 368

← 1 2 3 →