Trigonometric Approximation and 2π-Periodic Neural Network Approximation
DOI:
https://doi.org/10.29304/jqcm.2023.15.2.1254Keywords:
Neural approximation,, Trigonometric approximation, Best approximationAbstract
Many articles studied best trigonometric approximation and many researchers worked on the neural network approximation, but no one related the best trigonometric approximation to neural network approximation. We define trigonometric activation function, then we use it to obtain neural network, which we use it as a best approximation for functions in spaces for . That what we shall introduce in our work have.
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References
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[7] H. A. Almurieb and E. S. Bhaya, “Best neural simultaneous approximation,” Indonesian Journal of Electrical Engineering and Computer Science, vol 20, (2020), pp. 1584-1590.
[8] H. A. Almurieb and E. S. Bhaya, “SoftMax neural best approximation,” in IOP Conference Series: Materials Science and Engineering, Karbala, Iraq, vol 871, (2020), 012040: IOP Publishing.
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[11] E. S. Bhaya and O. A. Al-Sammak, “Radial Basis Functions Neural Networks Convolution Approximation," Journal of Engineering and Applied Sciences, vol 13, (2018), pp. 8153 - 8158.
[12] E. S. Bhaya and Z. A. Sharba, “L_p_ approximation by ReLU neural networks," Karbala International Journal of Modern Science, vol 6, (2020), pp. 414e9.
[13] H. N. Kazem and E. S. Bhaya, “Finite fourier coefficients is best approximation to f∈ L(P,α,β)," Journal of Advanced Research in Dynamical and Control Systems, vol 12, (2020), pp. 193-199.
[2] R.B. Holmes, “Geometric functional analysis and its applications,” springer -Verlag, New York, (1975).
[3] G.G. Lorentz, “Approximation of functions,” Holt, Rine Hart, Winston, New York, (1966).
[4] H.N. NHASKAR, “Neural networks for optimal approximation of smooth and analytic functions,” neural computation, vol 8, (1996), pp. 164-177.
[5] H.N. MHASKAR and C.A. Micchelli, “Degree of approximation by neural and translation networks with a single hidden layer,” Advances in Applied Mathematics, vol 16, (1995), pp. 151-183.
[6] S. M. Aboud and E. S. Bhaya, “Approximation of Fourier series in terms of functions in Lp-Spaces,” International Journal of Nonlinear Analysis and Applications, vol 12, (2021), pp. 897-911.
[7] H. A. Almurieb and E. S. Bhaya, “Best neural simultaneous approximation,” Indonesian Journal of Electrical Engineering and Computer Science, vol 20, (2020), pp. 1584-1590.
[8] H. A. Almurieb and E. S. Bhaya, “SoftMax neural best approximation,” in IOP Conference Series: Materials Science and Engineering, Karbala, Iraq, vol 871, (2020), 012040: IOP Publishing.
[9] E. Bhaya and O. Al-sammak, “Approximation by Regular Neural Networks in Terms of Dunkl Transform,” Research Journal of Applied Sciences, vol 11, (2016), pp. 833-941.
[10] E. S. Bhaya and Z. H. Abd Al-Sadaa, “Trigonometric Neural Networks Lp, p< 1 Approximation" in Journal of Physics: Conference Series, Iraq, vol 1591, (2020), 012060: IOP Publishing.
[11] E. S. Bhaya and O. A. Al-Sammak, “Radial Basis Functions Neural Networks Convolution Approximation," Journal of Engineering and Applied Sciences, vol 13, (2018), pp. 8153 - 8158.
[12] E. S. Bhaya and Z. A. Sharba, “L_p_ approximation by ReLU neural networks," Karbala International Journal of Modern Science, vol 6, (2020), pp. 414e9.
[13] H. N. Kazem and E. S. Bhaya, “Finite fourier coefficients is best approximation to f∈ L(P,α,β)," Journal of Advanced Research in Dynamical and Control Systems, vol 12, (2020), pp. 193-199.
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Published
2023-09-25
How to Cite
Bhay, E. S., & Mahdi, S. S. (2023). Trigonometric Approximation and 2π-Periodic Neural Network Approximation. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(2), Math Page 118–131. https://doi.org/10.29304/jqcm.2023.15.2.1254
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Math Articles
