【摘要】 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。更多还原

【Abstract】 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.更多还原