Abstract
With the best trigonometric polynomial approximation as a metric, the rate of approximation of the one-hidden-layer feedforward neural networks to approximate an integrable function is estimated by using a constructive approach in this paper. The obtained result shows that for any 2π-periodic integrable function, a neural networks with sigmoidal hidden neuron can be constructed to approximate the function, and that the rate of approximation do not exceed the double of the best trigonometric polynomial approximation of function.
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This paper was supported by the National Basic Research Program of China (973 Program) under Grant No. 2007CB311000, the Natural Science Foundation of China under Grant Nos. 11001227, 60972155, 10701062, the Key Project of Chinese Ministry of Education under Grant No. 108176, Natural Science Foundation Project of CQ CSTC Nos. CSTC 2009BB2306, CSTC2009BB2305, the Fundamental Research Funds for the Central Universities under Grant No. XDJK2010B005, XDJK2010C023.
This paper was recommended for publication by Editor Jinhu LÜ.
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Wang, J., Xu, Z. Neural networks and the best trigomometric approximation. J Syst Sci Complex 24, 401–412 (2011). https://doi.org/10.1007/s11424-011-8080-x
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DOI: https://doi.org/10.1007/s11424-011-8080-x