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

L. Li; B. Han; W. Wang

doi:10.1016/j.cam.2006.07.022

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

L. Li^*
, B. Han
, W. Wang

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

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 δ we prove that the convergence rate is O (δ^{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.

Original language	English
Pages (from-to)	341-357
Number of pages	17
Journal	Journal of Computational and Applied Mathematics
Volume	206
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2006.07.022
State	Published - 1 Sep 2007

Keywords

Continuous methods
Ill-posed problems
R-K type Landweber method

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10.1016/j.cam.2006.07.022

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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 δ we prove that the convergence rate is O (δ2 / 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.",

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AU - Han, B.

AU - Wang, W.

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N2 - 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 δ we prove that the convergence rate is O (δ2 / 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.

AB - 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 δ we prove that the convergence rate is O (δ2 / 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.

KW - Continuous methods

KW - Ill-posed problems

KW - R-K type Landweber method

UR - https://www.scopus.com/pages/publications/34249298693

U2 - 10.1016/j.cam.2006.07.022

DO - 10.1016/j.cam.2006.07.022

M3 - 文章

AN - SCOPUS:34249298693

SN - 0377-0427

VL - 206

SP - 341

EP - 357

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

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

Abstract

Keywords

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