三角基函数神经网络算法在数值积分中的应用研究
Numerical Integration Study Based on Triangle Basis Neural Network Algorithm
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摘要: 该文提出了一种基于三角基函数神经网络算法求解数值积分的新方法,提出并证明了神经网络算法的收敛定理和数值积分的求解定理及推论。最后给出了数值积分算例,并与传统计算方法作了比较分析.分析结果表明,该文提出的数值积分方法计算精度高,适应性强,而且不需要知道被积函数,因此该数值积分算法在电子学等工程实际中有较大的应用价值。Abstract: A new appproach to solve numerical integration is developsed in this paper, based on the algorithm of neural networks with triangle basis functions. The convergence theorem of the neural networks algorithm and the theorem of numerical integration solution and its inferences are presented and proved. By the examples of numerical integration the comparison is carried out with tradional methods. The results show that the numerical integration approach has the characteristics such as high precision, strong adaptablity, and the intergration of unknown fountions can be solved. Therefore, the numerical integration approach values significantly in many engineering applications, such as electronics, etc.
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Burden R L, Faires J D. Numerical Analysis(Seventh Edition)[M]. Brooks/Cole, Thomson Learning, Inc., 2001: 186-226.[2]王能超.数值分析简明教程[M].北京:高等教育出版社,1997:66-96.[3]沈剑华.数值计算基础[M].上海:同济大学出版社,1999:73-109.[4]林成森.数值计算方法(上)[M].北京:科学出版社,1998:173-215.[5]Burden R L, Faires J D. Numerical Analysis(Seventh Edition)[M]. Brooks/Cole, Thomson Learning, Inc., 2001: 206, 772.Burden R L, Faires J D. Numerical Analysis(Seventh Edition)[M]. Brooks/Cole, Thomson Learning, Inc., 2001: 212.Burden R L, Faires J D. Numerical Analysis(Seventh Edition)[M]. Brooks/Cole, Thomson Learning, Inc., 2001: 190.[6]Oppenheim A V,Willsky A S,Hamid Nawab W S著,刘树棠译.信号与系统(第二版)[M].西安:西安交通大学出版社,1998:71-72. -
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