卷积神经网络的方程组求解  

Convolutional Neural Network for Solving Linear Systems

作　　者：周伟 陆玉稳 ZHOU Wei;LU Yuwen(Electronic Information School,Shandong University of Business and Technology,Yantai Shandong 264000,China)

机构地区：[1]山东工商学院信息与电子工程学院,山东烟台264000

出　　处：《计算机与网络》2018年第22期69-72,共4页Computer & Network

摘　　要：通过迭代求解方程组的解,提出了一种基于卷积神经网络求解线性方程组的病态方程组的方法,由于条件数过大,影响求解的精度,将求解方程组的过程转换为神经网络学习的过程。通过神经网络学习同目标数据形成一种映射关系,用最小化误差来实现参数优化,把方程组求解的问题进而转换成参数的优化问题,求得目标解。卷积神经网络的参数共享机制在高维的矩阵计算中减小了计算量,提高了计算效率。For solving the equations with iterative methods, this paper proposes a method based on convolutional neural network to solve ill-conditioned equations of linear equations. Because the too large condition number of ill-conditioned equations affects the accuracy of the solution, the process is transformed into a process of neural network learning. A mapping relationship is formed between neural network learning and target data to minimize the error for parameter optimization, the problem of the equation set is converted into a parameter optimization problem, and the target solution is obtained. The parameter sharing mechanism of convolutional neural networks reduces the amount of computation in high-dimensional matrix calculations and improves the efficiency of calculations.

关 键 词：卷积神经网络 病态方程组 参数优化 线性方程组 条件数 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]