解不适定算子方程的一个定常二步隐式迭代法  

A STATIONARY TWO-STEP IMPLICIT ITERATIVE METHOD FOR ILL-POSED OPERATOR EQUATIONS

作　　者：唐建国[1] 贺国强[1] 

机构地区：[1]上海大学数学系,上海200436

出　　处：《计算数学》2000年第4期473-486,共14页Mathematica Numerica Sinica

基　　金：国家自然科学基金!(19671050);湖南省教委青年骨干教师基金资助项目.

摘　　要：On the basis of an implicit iterative method for ill-posed operator equations, we introduce a relaxation factor w and a weighted factor μ, and obtain a stationary two-step implicit iterative method. The range of the factors which guarantee the convergence of iteration is explored. We also study the convergence properties and rates for both non-perturbed and perturbed equations. An implementable algorithm is presented by using Morozov discrepancy principle. The theoretical results show that the convergence rates of the new methods always lead to optimal convergent rates which are superior to those of the original one after choosing suitable relaxation and weighted factors. Numerical examples are also given, which coincide well with the theoretical results.On the basis of an implicit iterative method for ill-posed operator equations, we introduce a relaxation factor w and a weighted factor μ, and obtain a stationary two-step implicit iterative method. The range of the factors which guarantee the convergence of iteration is explored. We also study the convergence properties and rates for both non-perturbed and perturbed equations. An implementable algorithm is presented by using Morozov discrepancy principle. The theoretical results show that the convergence rates of the new methods always lead to optimal convergent rates which are superior to those of the original one after choosing suitable relaxation and weighted factors. Numerical examples are also given, which coincide well with the theoretical results.

关 键 词：不适定问题 隐式迭代法 二步迭代法 松驰因子 加权因子 算子方程 

分 类 号：O241[理学—计算数学]