A Runge-Kutta type modified Landweber method for nonlinear ill-posed operator equations

作者：Wang W; Han B^*; Li L

来源：Journal of Computational and Applied Mathematics, 2008, 212(2): 457-468.

DOI：10.1016/j.cam.2006.12.021

• ill-posed problem
• Runge-Kutta method
• modified Landweber method

In this paper, we investigate the convergence behavior of a Runge-Kutta type modified Landweber method for nonlinear ill-posed operator equations. In order to improve the stability and convergence of the Landweber iteration, a 2-stage Gauss-type Runge-Kutta method is applied to the continuous analogy of the modified Landweber method, to give a new modified Landweber method, called R-K type modified Landweber method. Under some appropriate conditions, we prove the convergence of the proposed method. We conclude with a numerical example confirming the theoretical results, including comparisons to the modified Landweber iteration.

• 出版日期2008-3-1
• 单位哈尔滨工业大学