非线性反问题求解的参数微分正则化方法

讨论了非线性反问题的求解问题,将具有大范围收敛特性的同伦方法引入到非线性反问题的求解之中,籍此克服非线性反问题常规求解过程中局部收敛的缺陷;结合吉洪诺夫正则化方法,以解决计算Frechet导数时病态的问题.在此基础上,提出了一种用于求解非线性反问题的参数微分正则化方法,给出其构造过程,并且证明了参数微分正则化方法解的存在性和收敛性.

The parameter differential regularization method for solving nonlinear inverse problems

The problem of solving nonlinear inverse problem is considered.In order to overcome the defects of local convergence of conventional methods,the homotopy method which has widely convergent property is applied,and to avoid the ill-posed inversion of the Frechet derivate operator,the Tikhonov regularization method is also introduced here.On the basis of homotopy and regularization methods,a widely convergence inversion scheme for solving nonlinear inverse problems called parameter differential regularization method is developed.The formation of it and the proof of its convergence theorem are given.