解非线性不适定问题的一种正则化方法  

A regularization method for solving nonlinear inverse problems

作　　者：王美吉[1] 潘状元[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,哈尔滨150080

出　　处：《西安工程大学学报》2013年第5期675-679,共5页Journal of Xi’an Polytechnic University

摘　　要：研究了在实Hilbert空间中,求解非线性不适定问题的方法.通过对修正的三阶牛顿法进行Tikhonov正则化,得到新的迭代格式.在适当的条件下选取正则化参数,应用广义偏差准则,得出该迭代格式是单调的且是收敛性的.结果表明此迭代格式可应用于求解非线性不适定问题.A method for solving nonlinear ill-posed problems in real Hilbert space was mainly studied. Through Tikhonov regularizing the modified Newton method,an iterative form was obtained. The regularization parameter was chose under suitable conditions, and the generalized error criterion was used, so that the iterative scheme is monotone and convergence. From the result it could be seen that the nonlinear ill-posed problems can be solved by using the iterative scheme.

关 键 词：非线性不适定问题 正则化 收敛性 

分 类 号：O241.1[理学—计算数学]