Have a personal or library account? Click to login

Hyperbolic Tangent Like Relied Banach Space Valued Neural Network Multivariate Approximations

Open Access
|May 2023

References

  1. G.A. Anastassiou, Moments in Probability and Approximation Theory, Pitman Research Notes in Math., Vol. 287, Longman Sci. & Tech., Harlow, U.K., 1993.
  2. G.A. Anastassiou, Rate of convergence of some neural network operators to the unitunivariate case, J. Math. Anal. Appl. 212 (1997), 237-262.
  3. G.A. Anastassiou, Quantitative Approximations, Chapman&Hall/CRC, Boca Raton, New York, 2001.
  4. G.A. Anastassiou, Inteligent Systems: Approximation by Artificial Neural Networks, Intelligent Systems Reference Library, Vol. 19, Springer, Heidelberg, 2011.
  5. G.A. Anastassiou, Univariate hyperbolic tangent neural network approximation, Mathematics and Computer Modelling 53 (2011), 1111-1132.
  6. G.A. Anastassiou, Multivariate hyperbolic tangent neural network approximation, Computers and Mathematics 61 (2011), 809-821.
  7. G.A. Anastassiou, Multivariate sigmoidal neural network approximation, Neural Networks 24 (2011), 378-386.
  8. G.A. Anastassiou, Univariate sigmoidal neural network approximation, J. Comput. Anal. Appl. 14 (4) (2012), 659-690.
  9. G.A. Anastassiou, Approximation by neural networks iterates, Advances in Applied Mathematics and Approximation Theory, pp. 1-20, Springer Proceedings in Math. & Stat., Springer, New York, 2013, Eds. G. Anastassiou, O. Duman.
  10. G.A. Anastassiou, Intel ligent Systems II: Complete Approximation by Neural Network Operators, Springer, Heidelberg, New York, 2016.
  11. G.A. Anastassiou, Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations, Springer, Heidelberg, New York, 2018.
  12. G.A. Anastassiou, General Multivariate arctangent function activated neural network approximations, J. Numer. Anal. Approx. Theory 51 (1) (2022), 37-66.
  13. G.A. Anastassiou, General sigmoid based Banach space valued neural network approximation, J. Comput. Anal. Appl., accepted for publication, 2022.
  14. H. Cartan, Differential Calculus, Hermann, Paris, 1971.
  15. Z. Chen, F. Cao, The approximation operators with sigmoidal functions, Computers and Mathematics with Applications 58 (2009), 758-765.
  16. D. Costarelli, R. Spigler, Approximation results for neural network operators activated by sigmoidal functions, Neural Networks 44 (2013), 101-106.
  17. D. Costarelli, R. Spigler, Multivariate neural network operators with sigmoidal activation functions, Neural Networks 48 (2013), 72-77.
  18. S. Haykin, Neural Networks: A Comprehensive Foundation (2 ed.), Prentice Hall, New York, 1998.
  19. W. McCulloch, W. Pitts, A logical calculus of the ideas immanent in nervous activity, Bulletin of Mathematical Biophysics 7 (1943), 115-133.
  20. T.M. Mitchell, Machine Learning, WCB-McGraw-Hill, New York, 1997.
  21. L.B. Rall, Computational Solution of Nonlinear Operator Equations, John Wiley & Sons, New York, 1969.
DOI: https://doi.org/10.2478/awutm-2023-0005 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Page range: 45 - 68
Published on: May 3, 2023
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2023 George A. Anastassiou, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.