A Runge-Kutta type modified Landweber method for nonlinear ill-posed operator equations
A Runge-Kutta type modified Landweber method for nonlinear ill-posed operator equations
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DOI：
10.1016/j.cam.2006.12.021
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发表时间：
2008-02
影响因子：
2.4
通讯作者：
Wei Wang;Han Bing;Li Li-Li
中科院分区：
文献类型：
--
作者：
Wei Wang;Han Bing;Li Li-Li
本文研究了非线性不适定算子方程的Runge-Kutta型修正Landweber方法的收敛性。为了提高Landweber迭代法的稳定性和收敛性，将两步Gauss型Runge-Kutta方法应用于修正Landweber方法的连续模拟，给出了一种新的修正Landweber方法，称为R-K型修正Landweber方法。在适当的条件下，证明了该方法的收敛性.最后，我们的数值例子证实了理论结果，包括比较修改后的Landweber迭代。
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.