计算机与数字工程2025，Vol.53Issue(3)：632-636,691,6.DOI:10.3969/j.issn.1672-9722.2025.03.004
基于神经网络的病态线性方程组求解
Solving Ill-conditioned Linear Equations Based on Neural Network
摘要
Abstract
When there are errors in its'coefficient matrix and the right-end vector of the ill-conditioned linear equations,the numerical solution has the problems of instability and even distortion.Addressing these issues,this paper proposes a SFNN(Sin-gle-Layer Feedforward Neural Network),in which the coefficient matrix of the ill-conditioned linear equations is used as the input of the SFNN and the solution of the ill-conditioned linear equations is used as the weight of the SFNN.Employing cross-entropy cost function as the SFNNs'objective function to be optimized and gradient descent method as the SFNNs'learning algorithm,the SFNN completes the solution of ill-conditioned linear equations.Finally,taking ill-conditioned linear equations constructed by Hilbert matrix,Vandermonde matrix and Pascal matrix as test case respectively,the SFNN algorithm is verified.The experimental results show that the proposed algorithm is effective for addressing severe ill-conditioned linear equations.关键词
单层前馈神经网络/病态线性方程组/高斯白噪声/梯度下降法Key words
SFNN/ill-conditioned linear equations/white Gaussian noise/gradient descent method分类
信息技术与安全科学引用本文复制引用
李鹏飞,张强,王辉..基于神经网络的病态线性方程组求解[J].计算机与数字工程,2025,53(3):632-636,691,6.基金项目
黑龙江省自然科学基金项目(编号:F2018003)资助. （编号:F2018003）
