一类基于积分平均值的函数重构

上海大学学报(自然科学版) ›› 2010, Vol. 16 ›› Issue (2): 157-162.

一类基于积分平均值的函数重构

孙士国,康传刚,贺国强

上海大学理学院，上海 200444

收稿日期:2008-11-12 出版日期:2010-04-20 发布日期:2010-04-20
通讯作者: 贺国强(1946～)，男，教授，博士生导师,研究方向为不适定问题与反问题. E-mail:gqhe@staff.shu.edu.cn

A Type of Reconstruction Methods of Function Based on Integral Average Values

SUN Shi-Guo, KANG Chuan-Gang, HE Guo-Qiang

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2008-11-12 Online:2010-04-20 Published:2010-04-20

摘要/Abstract

摘要：

考虑一类基于带有扰动的积分平均值的函数重构方法,从抽象算子方程的角度分析解决此类问题.证明解算子与网络步长无关的有界性,从而证明所讨论的问题的适定性,表明求解过程不需要正则化,大大简化了算法.最后,给出数值例子验证所讨论的方法的有效性.

关键词: 积分平均值;函数重构;解算子有界性;适定性;误差分析

Abstract:

A reconstruction problem of function from integral average values with perturbation is considered, and propose a type of reconstruction method. From the abstract operator equation, we analyze and solve this type of problem, and show that the solution operator is bounded regardless of the grid size. Therefore the problem under consideration is well-posed. The method of solving this problem does not need regularization, thus greatly simplifying the algorithm. Numerical results show that the method is effective. 

Key words: integral average value; reconstruction of function; boundedness of solution operator; well-posed; error analysis

中图分类号:

O 241.4

孙士国,康传刚,贺国强. 一类基于积分平均值的函数重构[J]. 上海大学学报(自然科学版), 2010, 16(2): 157-162.

SUN Shi-Guo, KANG Chuan-Gang, HE Guo-Qiang. A Type of Reconstruction Methods of Function Based on Integral Average Values[J]. Journal of Shanghai University（Natural Science Edition）, 2010, 16(2): 157-162.