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

✍ Scribed by W. Wang; B. Han; L. Li

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
189 KB
Volume
212
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

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