Neural-network Method Based on RLS Algorithm for Solving Hilbert Linear Systems of Equations

摘要

To aim at the ill-posed problems of linear system of equations, a neural-network method based on RLS algorithm (NN-RLS) is presented for solving Hilbert linear system of equations. The primary idea of the method is to improve conditional number of ill-conditioned matrix A, build neural-network model based on Hilbert linear system of equations, and use RSL algorithm to train neural-network weights, which is the solution of Hilbert linear system of equations. The results reveal that the proposed NN-RLS method is very simple and effective.