Neural network interpolation operators of multivariate functions

In this paper, we introduce a type of multivariate neural network interpolation operators Fn,σ(f) activated by some newly defined sigmoidal functions, and give both the direct and the converse results of the approximation by Fn,σ(f) for multivariate continuous functions. We also introduce a Kantorov...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2023-10, Vol.431, p.115266, Article 115266
Main Authors: Wang, Guoshun, Yu, Dansheng, Guan, Lingmin
Format: Article
Language:English
Subjects:
Interpolation
Neural network operators
Sigmoidal function
Uniform approximate
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Summary:In this paper, we introduce a type of multivariate neural network interpolation operators Fn,σ(f) activated by some newly defined sigmoidal functions, and give both the direct and the converse results of the approximation by Fn,σ(f) for multivariate continuous functions. We also introduce a Kantorovich type variant of Fn,σ(f), and establish both the direct theorem and the converse theorem of approximation by the Kantorovich type operators in Lp spaces with 1≤p
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2023.115266