Solving Ill-conditioned Linear Equations Based on Neural Network
LI Pengfei
ZHANG Qiang
WANG Hui
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.
Keywords：SFNNill-conditioned linear equationswhite Gaussian noisegradient descent method
Publication Date：2025-03-20
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：6( 632-636,691 )