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

被引：5
|
作者：
Zhang, Rong [1 ,2 ]
Li, Fanchun [3 ]
Luo, Xingjun [4 ]
机构：
[1] Sun Yat Sen Univ, Sch Data & Comp Sci, Guangzhou 510006, Peoples R China
[2] Guangdong Prov Key Lab Computat Sci, Guangzhou 510275, Guangdong, Peoples R China
[3] Jiangxi Coll Appl Technol, Sch Social Management, Ganzhou 341000, Peoples R China
[4] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Peoples R China
来源：
MATHEMATICS | 2020年 / 8卷 / 02期
基金：
中国国家自然科学基金;
关键词：
nonlinear ill-posed integral equations; Landweber iteration; multiscale Galerkin method; generalized discrepancy principle; convergence rates; POSTERIORI PARAMETER CHOICE; TIKHONOV REGULARIZATION; SCHEME;
D O I：
10.3390/math8020221
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页数：17
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