求解非线性不适定问题的隐式迭代法  

Nonlinear Implicit Iterative Method for Solving Nonlinear Ill-Posed Problems

作　　者：柳建军[1,2] 贺国强[1] 康传刚[1] 

机构地区：[1]上海大学数学系,上海200444 [2]中国石油管道研究中心,河北廊坊065000

出　　处：《应用数学和力学》2009年第9期1107-1116,共10页Applied Mathematics and Mechanics

基　　金：上海市重点学科(第三期)资助项目(S30104);上海市教委重点学科建设资助项目(J50101)

摘　　要：将处理线性不适定算子方程的隐式迭代法推广到非线性不适定问题,证明了迭代解误差序列的单调性,并进一步利用迭代误差的单调性得出求解非线性不适定问题隐式迭代法对精确方程和扰动方程的收敛性.The implicit iterative method was extended for linear ill-posed operator equations to solve nonlinear ill-posed problems. It shows that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing. And with this monotonicity, the convergence of the new method for both of the exact and perturbed equations was proved.

关 键 词：非线性不适定问题 非线性隐式迭代法 单调性 收敛性 

分 类 号：O241[理学—计算数学]