R-K type Landweber method for nonlinear ill-posed problems

Authors:
L. Li;B. Han;W. Wang
Affiliations:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 1
Cited 3

Optimal a posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problems

SIAM Journal on Numerical Analysis

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

Journal of Computational and Applied Mathematics
An implicit Landweber method for nonlinear ill-posed operator equations

Journal of Computational and Applied Mathematics
Runge-Kutta type total variation regularization for nonlinear inverse problems

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper we propose the R-K type Landweber iteration and investigate the convergence of the method for nonlinear ill-posed problem F(x)=y where F:H-H is a nonlinear operator between Hilbert space H. Moreover, for perturbed data with noise level @d we prove that the convergence rate is O(@d^2^/^3) under appropriate conditions. Finally, the numerical performance of this R-K type Landweber iteration for a nonlinear convolution equation is compared with the Landweber iteration.