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

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

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 con...

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Main Authors: Rong Zhang, Fanchun Li, Xingjun Luo
Format: Article
Language:English
Published: MDPI AG 2020-02-01
Series:Mathematics
Subjects:
nonlinear ill-posed integral equations
landweber iteration
multiscale galerkin method
generalized discrepancy principle
convergence rates
Online Access:https://www.mdpi.com/2227-7390/8/2/221
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spelling doaj-31a7c14dc6d64e1caf917f8e2c8abf0f2020-11-25T02:05:26ZengMDPI AGMathematics2227-73902020-02-018222110.3390/math8020221math8020221Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber IterationRong Zhang0Fanchun Li1Xingjun Luo2School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, ChinaSchool of Social Management, Jiangxi College of Applied Technology, Ganzhou 341000, ChinaSchool of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, ChinaIn 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.https://www.mdpi.com/2227-7390/8/2/221nonlinear ill-posed integral equationslandweber iterationmultiscale galerkin methodgeneralized discrepancy principleconvergence rates
collection DOAJ
language English
format Article
sources DOAJ
author Rong Zhang
Fanchun Li
Xingjun Luo
spellingShingle Rong Zhang
Fanchun Li
Xingjun Luo
Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration
Mathematics
nonlinear ill-posed integral equations
landweber iteration
multiscale galerkin method
generalized discrepancy principle
convergence rates
author_facet Rong Zhang
Fanchun Li
Xingjun Luo
author_sort Rong Zhang
title Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration
title_short Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration
title_full Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration
title_fullStr Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration
title_full_unstemmed Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration
title_sort multiscale compression algorithm for solving nonlinear ill-posed integral equations via landweber iteration
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-02-01
description 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.
topic nonlinear ill-posed integral equations
landweber iteration
multiscale galerkin method
generalized discrepancy principle
convergence rates
url https://www.mdpi.com/2227-7390/8/2/221
work_keys_str_mv AT rongzhang multiscalecompressionalgorithmforsolvingnonlinearillposedintegralequationsvialandweberiteration
AT fanchunli multiscalecompressionalgorithmforsolvingnonlinearillposedintegralequationsvialandweberiteration
AT xingjunluo multiscalecompressionalgorithmforsolvingnonlinearillposedintegralequationsvialandweberiteration
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