preprint · arXiv (Cornell University) · 2014

Univariate error function based neural network approximation

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Abstract

Here we research the univariate quantitative approximation of real and complex valued continuous functions on a compact interval or all the real line by quasi-interpolation, Baskakov type and quadrature type neural network operators. We perform also the related fractional approximation. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its high order derivative or fractional derivatives. Our operators are defined by using a density function induced by the error function. The approximations are pointwise and with respect to the uniform norm. The related feed-forward neural networks are with one hidden layer.

Cite this paper

APA 7

Anastassiou, G. A. (2014). Univariate error function based neural network approximation. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1404.6449

MLA 9

Anastassiou, George A. “Univariate error function based neural network approximation.” arXiv (Cornell University), 2014, https://doi.org/10.48550/arxiv.1404.6449.

Chicago

Anastassiou, George A. 2014. “Univariate error function based neural network approximation.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1404.6449.

Harvard

Anastassiou, G.A. (2014) ‘Univariate error function based neural network approximation’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1404.6449.

BibTeX

@misc{anastassiou2014univariate,
  title = {{Univariate error function based neural network approximation}},
  author = {Anastassiou, George A.},
  journal = {arXiv (Cornell University)},
  year = {2014},
  doi = {10.48550/arxiv.1404.6449}
}

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