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

Rong Zhang, Fanchun Li and Xingjun Luo
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Rong Zhang: School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, China
Fanchun Li: School of Social Management, Jiangxi College of Applied Technology, Ganzhou 341000, China
Xingjun Luo: School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China

Mathematics, 2020, vol. 8, issue 2, 1-17

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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