摘要
科学与工程领域经常使用数值积分,为此提出了一种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αn并用傅立叶级数∑Nn=0αncos(nx)来近似未知函数f(x),然后用∑Nn=0α∫nbacos(nx)dx来近似积分∫baf(x)dx.提出并证明了神经网络算法的收敛性定理和数值积分的求解定理.数值积分算例验证了本文算法的有效性.研究结果表明,本文提出的数值积分方法有高的计算精度,在工程实际中有较大的应用价值.
Numerical integration is used in science and engineering. A new method for solving numerical integration is proposed. The main idea is to use a sum ∑n=0^N αncos（nx） to approximate a function f（x） by training the weights a. of neural networks, then let ∑n=0^N αn∫a^bcos（nx）dr to approximate∫a^bf（x）dx. The convergence theorem ot neural networks algorithm and the theorem for solving numerical integration are given and proved. This algorithm is validated by the simulation examples of numerical integration. The results show that numerical integration approach presented has high precision and important application value jn the engineering practice.
出处
《传感技术学报》
CAS
CSCD
北大核心
2006年第4期1187-1189,1194,共4页
Chinese Journal of Sensors and Actuators
基金
国家自然科学基金项目资助(60375001)
关键词
数值积分
神经网络
余弦基函数
收敛性
numerical integration
neural network
cosine basis functions
convergence
