基于动力系统求解线性不适定问题的一种迭代方法

上海大学学报(自然科学版)

基于动力系统求解线性不适定问题的一种迭代方法

孙晶，贺国强

上海大学理学院，上海 200444

收稿日期:2007-01-17 修回日期:1900-01-01 出版日期:2008-04-30 发布日期:2008-04-30
通讯作者: 贺国强

An Iterative Method for Solving Linear Ill-Posed Problems Based on Dynamical Systems

SUN Jing, HE Guo-qiang

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2007-01-17 Revised:1900-01-01 Online:2008-04-30 Published:2008-04-30

摘要/Abstract

摘要： 该文基于一个抽象微分方程的二阶RungeKutta方法，构造一种求解线性不适定算子方程的迭代方法——中点法，并讨论此方法的收敛性及收敛速率，数值试验的结果也与该理论相符.

关键词: 残差准则, 抽象微分方程, 二阶RungeKutta方法, 收敛速率

Abstract: This paper proposes an iterative method for solving illposed operator equations based on dynamical systems and discuss the convergence properties and convergence rates of the method. Numerical examples are given, which is in agreement with the theoretical results.

Key words: convergence rates, discrepancy principle, Runge-Kutta two-order method, abstract differential equation

中图分类号:

O242

孙晶;贺国强. 基于动力系统求解线性不适定问题的一种迭代方法[J]. 上海大学学报(自然科学版).

SUN Jing;HE Guo-qiang. An Iterative Method for Solving Linear Ill-Posed Problems Based on Dynamical Systems[J]. Journal of Shanghai University（Natural Science Edition）.