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中文摘要：
提出了一种高精度求解数值积分的新方法，其主要思想是通过训练神经网络权值并用傅立叶级数来近似未知函数，然后用傅立叶级数的积分来近似未知函数的积分,提出并证明了该算法的收敛性定理和数值积分的求解定理．仿真结果表明，与其它方法相比，本文提出的数值积分方法有计算精度高的特点，因而在工程实际中有较大的应用价值.
英文摘要：
A new approach with high accuracy for solving numerical integration was presented. The idea was to use a Fourier series to approximate a unknown function by training the weights of neural networks, and then to use the Fourier series trained by neural network algorithm to approximate the integration of the unknown function. The convergence theorem of neural networks algorithm and the theorem of numerical integration were presented and proved. Simulation results showed that the numerical integration approach presented in the paper had higher accuracy than other methods, so it will be very valuable in many engineering applications.
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