On the Representation by Bivariate Ridge Functions

被引：1
作者：
Aliev, R. A. [1 ,2 ]
Asgarova, A. A. [3 ]
Ismailov, V. E. [4 ]
机构：
[1] Azerbaijan Natl Acad Sci, Inst Math & Mech, Baku, Azerbaijan
[2] Baku State Univ, Baku, Azerbaijan
[3] Azerbaijan Univ Languages, Baku, Azerbaijan
[4] Natl Acad Sci Azerbaijan, Inst Math & Mech, Baku, Azerbaijan
来源：
UKRAINIAN MATHEMATICAL JOURNAL | 2021年 / 73卷 / 05期
关键词：
NEURAL-NETWORKS; FINITE SUMS; APPROXIMATION; RECONSTRUCTION;
D O I：
10.1007/s11253-021-01952-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the problem of representation of bivariate functions by sums of ridge functions. It is shown that if a function from a certain class of smoothness is represented by the sum of finitely many ridge functions with arbitrary behaviors, then it can be also represented as the sum of ridge functions of the same class of smoothness. As an example, this result is applied to a homogeneous partial differential equation with constant coefficients.
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页码：675 / 685
页数：11
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