Rates of approximation by neural network interpolation operators

Yunyou Qian and Dansheng Yu

Applied Mathematics and Computation, 2022, vol. 418, issue C

Abstract: We construct neural network interpolation operators with some newly defined activation functions, and give the approximation rate by the operators for continuous functions. By adding some smooth assumptions on the activation function, we establish two important inequalities of the derivative of the operators. With these two inequalities, by using K-functional and Berens–Lorentz lemma in approximation theory, we obtain the converse theorem of approximation by the operators. To approximate smooth functions, we further introduce special combinations of the operators, which can be regarded as FNNs with four layers, and can approximate the object function and its derivative simultaneously. Finally, we introduce a Kantorovich type variant of the operators. We establish both the direct theorem and the converse theorem of approximation by the Kantorovich type operators in Lp spaces with 1≤p≤∞.

Keywords: Sigmoidal function; Neural network operators; Interpolation; Uniform approximate; Simultaneous approximation (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300321008638
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321008638

DOI: 10.1016/j.amc.2021.126781

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().