Interpolation for Neural Network Operators Activated by Smooth Ramp Functions

被引：0

作者：

Baxhaku, Fesal ^{[1
]}

Berisha, Artan ^{[2
]}

Baxhaku, Behar ^{[2
]}

机构：

[1] Univ Prizren, Dept Comp Sci, Prizren 20000, Kosovo

[2] Univ Prishtina Hasan Prishtina, Dept Math, Prishtina 10000, Kosovo

来源：

COMPUTATION | 2024年 / 12卷 / 07期

关键词：

sigmoidal function; neural network operators; interpolation; modulus of continuity; asymptotic expansion; APPROXIMATION; CONVERGENCE;

D O I：

10.3390/computation12070136

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present article, we extend the results of the neural network interpolation operators activated by smooth ramp functions proposed by Yu (Acta Math. Sin.(Chin. Ed.) 59:623-638, 2016). We give different results from Yu (Acta Math. Sin.(Chin. Ed.) 59:623-638, 2016) we discuss the high-order approximation result using the smoothness of phi and a related Voronovskaya-type asymptotic expansion for the error of approximation. In addition, we showcase the related fractional estimates result and the fractional Voronovskaya type asymptotic expansion. We investigate the approximation degree for the iterated and complex extensions of the aforementioned operators. Finally, we provide numerical examples and graphs to effectively illustrate and validate our results.

引用

页数：20

共 32 条

[1] Rate of convergence of some neural network operators to the unit-univariate case [J].