An implicit Landweber method for nonlinear ill-posed operator equations

作者：Wang Wei; Han Bo^*

来源：Journal of Computational and Applied Mathematics, 2009, 230(2): 607-613.

DOI：10.1016/j.cam.2008.12.016

• Ill-posed problem
• Landweber iteration
• Implicit method

In this paper, we are interested in the solution of nonlinear inverse problems of the form F(x) = y. We propose an implicit Landweber method, which is similar to the third-order midpoint Newton method in form, and consider the convergence behavior of the implicit Landweber method. Using the discrepancy principle as a stopping criterion, we obtain a regularization method for ill-posed problems. We conclude with numerical examples confirming the theoretical results, including comparisons with the classical Landweber iteration and presented modified Landweber methods.

• 出版日期2009-8-15
• 单位哈尔滨工业大学