The construction and approximation of feedforward neural network with hyp erb olic tangent function |
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Authors: | CHEN Zhi-xiang CAO Fei-long |
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Institution: | 1. Department of Mathematics, Shaoxing University, Shaoxing 312000, China 2. Department of Mathematics, China Jiliang University, Hangzhou 310018, China |
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Abstract: | In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tangent activation functionFirstly, an equation of partitions of unity for the hyperbolic tangent function is givenThen, two kinds of quasi-interpolation type neural network operators are constructed to approximate univariate and bivariate functions, respectivelyAlso, the errors of the approximation are estimated by means of the modulus of continuity of functionMoreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated. |
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Keywords: | Hyperbolic tangent function neural networks approximation modulus of continuity |
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