求解非线性方程的简化动力系统方法  

A Simplified Dynamical Systems Method for Solving Nonlinear Equation

作　　者：黄静月 罗兴钧[1] 张荣[1] Jing Yue HUANG;Xing Jun LUO;Rong ZHANG(School of Mathematics and Computer Sciences,Gannan Normal University,Ganzhou 341000,P.R.China)

机构地区：[1]赣南师范大学数学与计算机科学学院,赣州341000

出　　处：《数学学报（中文版）》2023年第2期223-238,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11761010)。

摘　　要：本文研究求解非线性方程F(u)=f的简化动力系统方法,在算子F和精确解y满足一定的条件下,给出了动力系统方程解的误差估计,提出了正则化参数后验选择的偏差原理,确保了动力系统方程解的最优收敛率.与传统动力系统方法比较,简化动力系统方法减少了导数的计算量.A simplified dynamical systems method for solving the nonlinear equation F(u)=f is studied in this paper.Under certain conditions of the operator F and the exact solution y,the error estimate of the solution of the dynamical systems equation is given,and the discrepancy principle of the posterior selection of regularized parameter is proposed to ensure the optimal rate of convergence of the solution of the dynamical systems equation.Compared with the traditional dynamical systems method,the simplified dynamical systems method reduces the computation amount of derivatives.

关 键 词：非线性方程 不适定问题 收敛率 简化动力系统方法 

分 类 号：O241.1[理学—计算数学]