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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Bibliographic Details
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
Description
Summary: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.
ISSN:2227-7390

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