解非线性不适定问题的一种正则化方法

A regularization method for solving nonlinear ill-posed problems

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 is mainly studied. Through Tikhonov regularizing the modified Newton method,an iterative form is obtained. The regularization parameter is chosen under suitable conditions, and the generalized error criterion is used, so that the iterative scheme is monotone and convergence is obtained. From the result it can be seen that the nonlinear ill-posed problems can be solved by using the iterative scheme.