一种解非线性反问题的正则化方法

A regularization method for solving nonlinear inverse problems

求解实H ilbert空间中的非线性不适定算子方程F(x)=y.对修正的三阶牛顿法进行正则化,以获得新的修正Levenberg-Marquardt迭代格式。在适当的条件下应用广义偏差原则,对该迭代格式的收敛性进行了分析与证明,并通过求解参数识别问题说明该方法的有效性。

In order to solve the nonlinear ill -posed operator equation in Hilbert space, a modified Newton method is regularized to obtain a modified Levenberg - Marquardt iterative form. Using the discrepancy principle as a stopping criterion, the convergence of this regularization method is investigated under appropriate assumptions. Numerical experiments solving parameter identification problem are presented to illustrate the performance of the method and show its advantages.