Richards's curve induced Banach space valued ordinary and fractional neural network approximation.

IF 1.8 2区 数学 Q1 MATHEMATICS
George A Anastassiou, Seda Karateke
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引用次数: 2

Abstract

Here we perform the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its Banach space valued high order derivative or fractional derivatives. Our operators are defined by using a density function generated by the Richards curve, which is generalized logistic function. The approximations are pointwise and of the uniform norm. The related Banach space valued feed-forward neural networks are with one hidden layer.

Richards曲线诱导Banach空间值普通和分数神经网络逼近。
本文利用拟插值Banach空间值神经网络算子,对紧区间或实直线上的Banach空间值连续函数进行了普通和分数的单变量定量逼近。这些近似是通过建立Jackson型不等式推导出来的,该不等式涉及接合函数或其Banach空间值高阶导数或分数阶导数的连续性模。我们的算子是用Richards曲线生成的密度函数来定义的,这是一个广义逻辑函数。近似是逐点的,并且是一致范数的。相关的Banach空间值前馈神经网络只有一个隐藏层。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
4.70
自引率
17.20%
发文量
151
审稿时长
>12 weeks
期刊介绍: The journal publishes, in English language only, high-quality Research Articles covering Algebra; Applied Mathematics; Computational Sciences; Geometry and Topology; Mathematical Analysis; Statistics and Operations Research. Also featured are Survey Articles in every mathematical field.
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