Quantitative Approximation by a Kantorovich-Shilkret quasi-interpolation neural network operator
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George A. Anastassiou
ganastss@memphis.edu
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DOI:
https://doi.org/10.4067/S0719-06462018000300001Abstract
In this article we present multivariate basic approximation by a Kantorovich-Shilkret type quasi-interpolation neural network operator with respect to supremum norm. This is done with rates using the multivariate modulus of continuity. We approximate continuous and bounded functions on â„N, N ∈ â„•. When they are additionally uniformly continuous we derive pointwise and uniform convergences.
Keywords
M. Abramowitz, I.A. Stegun, eds, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York, Dover Publication, 1972.
G.A. Anastassiou, Univariate error function based neural network approximation, Indian J. ofMath., Vol. 57, No. 2 (2015), 243-291.
L.C. Andrews,Special Functions of Mathematics for Engineers, Second edition, Mc Graw-Hill, New York, 1992.
I.S. Haykin, Neural Networks: A Comprehensive Foundation(2 ed.), Prentice Hall, New York,1998.
W. McCulloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity,Bulletin of Mathematical Biophysics, 7 (1943), 115-133.
T.M. Mitchell,Machine Learning, WCB-McGraw-Hill, New York, 1997.
Niel Shilkret, Maxitive measure and integration, Indagationes Mathematicae, 33 (1971), 109-116.
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