Functional Network Construction and Approximation Algorithm for Polynomial Functions
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As for the optimization of polynomial function algorithm, artificial neural network is an important method to solve the problem of function approximation. However, the traditional learning neural network has some defects, such as being very sensitive to the initial weight and easy to converge to the local minimum; Slow convergence or even no convergence; Over fitting and over training; The number of hidden nodes in the network is uncertain. To solve the above problems, a three-layer functional network and approximation algorithm of polynomial function are proposed, and how to determine the number of calculation units in the middle hidden layer is given. The proposed algorithm can approximate polynomial function with arbitrary accuracy, and has fast convergence speed and good performance, which overcomes the shortcomings of artificial neural network. The example analysis shows that the algorithm is very effective, fast convergence speed and high calculation accuracy. The proposed polynomial functional regression functional network model and learning algorithm have important guiding significance for the research of computer algebra.
Polynomial function, Functional network, Approximation algorithm, Network construction