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Multivariate Jackson-type inequality for a new type neural network approximation

Authors
Journal
Applied Mathematical Modelling
0307-904X
Publisher
Elsevier
Identifiers
DOI: 10.1016/j.apm.2014.05.018
Keywords
  • Neural Networks
  • Jackson-Type Inequality
  • Error Estimate
  • Sigmoidal Function
Disciplines
  • Computer Science

Abstract

Abstract In this paper, we introduce a new type neural networks by superpositions of a sigmoidal function and study its approximation capability. We investigate the multivariate quantitative constructive approximation of real continuous multivariate functions on a cube by such type neural networks. This approximation is derived by establishing multivariate Jackson-type inequalities involving the multivariate modulus of smoothness of the target function. Our networks require no training in the traditional sense.

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