Multivariate neural network interpolation operators


Kadak U.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.414, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 414
  • Publication Date: 2022
  • Doi Number: 10.1016/j.cam.2022.114426
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Interpolation operators, Image interpolation, Image processing, Neural network interpolation operators, Multivariate fractional calculus, FRACTIONAL CALCULUS, APPROXIMATION, BOUNDS
  • Gazi University Affiliated: Yes

Abstract

In this paper, we introduce and study fractional neural network interpolation operators activated by a sigmoidal function belonging to the extended class of multivariate sigmoidal functions. We examine the rates of approximation by the operators in L-p- spaces using the modulus of continuity. Moreover, we give some special examples with graphics for the extended class of multivariate sigmoidal functions, and present some illustrative examples to demonstrate the interpolation quality of the operators based on various activation functions. Finally, as an application, we present an efficient image processing algorithm by the proposed neural network interpolation operators for both general and medical gray-level images.(C) 2022 Elsevier B.V. All rights reserved.