求解非线性不适定问题的连续Landweber型正则化方法(英文)  

Continuous Landweber type regularization method for solving nonlinear ill-posed problem

作　　者：曹莉[1,2] 王伟[1] 

机构地区：[1]哈尔滨工业大学土木工程学院,哈尔滨150001 [2]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2014年第2期165-170,共6页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the 51th Postdoctoral Science Foundation of China

摘　　要：提出一种用于求解非线性不适定问题的连续Landweber型正则化方法。在假定解是光滑的前提下,证明该方法的收敛性和稳定性。数值模拟表明,对该方法离散化后可得到二阶迭代格式,方法稳定,且在较少的迭代步数内收敛。A continuous Landweber type regularization method for solving nonlinear ill-posed prob- lems is proposed. Under the smoothness of the unknown solution, convergence and stability of the asymp- totical regularization method are given. Moreover, some numerical experiments are presented to illustrate that the 2-stage iterative regularization methods are stable and efficient in saving iteration steps.

关 键 词：非线性不适定问题 连续型方法 渐进正则化方法 修正Landweber方法 

分 类 号：O241.82[理学—计算数学]