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Open AccessArticle

Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration

by Rong Zhang 1,2,*, Fanchun Li 3 and Xingjun Luo 4
1
School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, China
2
Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, China
3
School of Social Management, Jiangxi College of Applied Technology, Ganzhou 341000, China
4
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 221; https://doi.org/10.3390/math8020221
Received: 2 January 2020 / Revised: 6 February 2020 / Accepted: 6 February 2020 / Published: 9 February 2020
(This article belongs to the Special Issue Inverse and Ill-posed Problems)
In this paper, Landweber iteration with a relaxation factor is proposed to solve nonlinear ill-posed integral equations. A compression multiscale Galerkin method that retains the properties of the Landweber iteration is used to discretize the Landweber iteration. This method leads to the optimal convergence rates under certain conditions. As a consequence, we propose a multiscale compression algorithm to solve nonlinear ill-posed integral equations. Finally, the theoretical analysis is verified by numerical results.
Keywords: nonlinear ill-posed integral equations; Landweber iteration; multiscale Galerkin method; generalized discrepancy principle; convergence rates nonlinear ill-posed integral equations; Landweber iteration; multiscale Galerkin method; generalized discrepancy principle; convergence rates
MDPI and ACS Style

Zhang, R.; Li, F.; Luo, X. Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration. Mathematics 2020, 8, 221.

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