Abstract
Here we study 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.
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References
M. Abramowitz, I.A. Stegun (eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications, New York, 1972)
G.A. Anastassiou, Rate of convergence of some neural network operators to the unit-univariate case. J. Math. Anal. Appli. 212, 237–262 (1997)
G.A. Anastassiou, Quantitative Approximations (Chapman & Hall/CRC, Boca Raton, New York, 2001)
G.A. Anastassiou, On right fractional calculus. Chaos, Solitons Fractals 42, 365–376 (2009)
G.A. Anastassiou, Fractional Differentiation Inequalities (Springer, New York, 2009)
G.A. Anastassiou, Fractional Korovkin theory. Chaos, Solitons Fractals 42(4), 2080–2094 (2009)
G.A. Anastassiou, Inteligent Systems: Approximation by Artificial Neural Networks, Intelligent Systems Reference Library, vol. 19 (Springer, Heidelberg, 2011)
G.A. Anastassiou, Fractional representation formulae and right fractional inequalities. Math. Comput. Model. 54(11–12), 3098–3115 (2011)
G.A. Anastassiou, Univariate hyperbolic tangent neural network approximation. Math. Comput. Model. 53, 1111–1132 (2011)
G.A. Anastassiou, Multivariate hyperbolic tangent neural network approximation. Comput. Math. 61, 809–821 (2011)
G.A. Anastassiou, Multivariate sigmoidal neural network approximation. Neural Networks 24, 378–386 (2011)
G.A. Anastassiou, Univariate sigmoidal neural network approximation. J. Comput. Anal. Appl. 14(4), 659–690 (2012)
G.A. Anastassiou, Fractional neural network approximation. Comput. Math. Appl. 64, 1655–1676 (2012)
G.A. Anastassiou, Univariate error function based neural network approximation. Indian J. Math. (2014)
L.C. Andrews, Special Functions of Mathematics for Engineers, 2nd edn. (Mc Graw-Hill, New York, 1992)
Z. Chen, F. Cao, The approximation operators with sigmoidal functions. Comput. Math. Appl. 58, 758–765 (2009)
K. Diethelm, The Analysis of Fractional Differential Equations, vol. 2004, Lecture Notes in Mathematics (Springer, Berlin, 2010)
A.M.A. El-Sayed, M. Gaber, On the finite caputo and finite riesz derivatives. Electron. J. Theor. Phys. 3(12), 81–95 (2006)
G.S. Frederico, D.F.M. Torres, Fractional optimal control in the sense of caputo and the fractional Noether’s theorem. Int. Math. forum 3(10), 479–493 (2008)
S. Haykin, Neural Networks: a Comprehensive Foundation, 2nd edn. (Prentice Hall, New York, 1998)
W. McCulloch, W. Pitts, A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 7, 115–133 (1943)
T.M. Mitchell, Machine Learning (WCB-McGraw-Hill, New York, 1997)
D.S. Mitrinovic, Analytical Inequalities (Springer, New York, 1970)
S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, (Gordon and Breach, Amsterdam, 1993) [English translation from the Russian, Integrals and Derivatives of Fractional Order and Some of Their Applications (Nauka i Tekhnika, Minsk, 1987)]
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Anastassiou, G.A. (2016). Univariate Error Function Based Neural Network Approximations. In: Intelligent Systems II: Complete Approximation by Neural Network Operators. Studies in Computational Intelligence, vol 608. Springer, Cham. https://doi.org/10.1007/978-3-319-20505-2_17
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DOI: https://doi.org/10.1007/978-3-319-20505-2_17
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