摘要
对紧算子方程的不适定性进行了详细的分析,证明了紧算子方程奇异值分解定理,并以一维热传导方程反问题为例,将其转化为紧算子方程,讨论了求解此反问题的最优估计及进行了误差分析,数值模拟表明了理论分析与实际应用的一致性.
The purpose of the paper is to discuss the ill-posedness and to prove the singular value decomposition theorem of compact operator equation.Then taking one-dimensional backward heat conduction problem for example,we translate it into compact operator equation and put forward an optimal estimate of which error analysis is also given for solving the ill-posed problem.Numerical simulation shows that the theoretical analysis is consistent with practical application.
出处
《应用泛函分析学报》
CSCD
2012年第2期140-146,共7页
Acta Analysis Functionalis Applicata
基金
陕西省教育厅基金(08JK388)
关键词
紧算子
反问题
不适定
正则化
正则参数
compact operator
inverse problem
ill-posed
regularization
regular parameter