Convergence analysis of a two-point gradient method for nonlinear ill-posed problems

被引：47

作者：

Hubmer, Simon ^{[1
]}

Ramlau, Ronny ^{[2
,3
]}

机构：

[1] Johannes Kepler Univ Linz, Doctoral Program Computat Math, Altenbergerstr 69, A-4040 Linz, Austria

[2] Johannes Kepler Univ Linz, Inst Ind Math, Altenbergerstr 69, A-4040 Linz, Austria

[3] Johann Radon Inst Linz, Altenbergerstr 69, A-4040 Linz, Austria

来源：

INVERSE PROBLEMS | 2017年 / 33卷 / 09期

基金：

奥地利科学基金会;

关键词：

two-point gradient method; Nesterov acceleration scheme; Landweber iteration; steepest descent; minimal error; regularization method; SPECT; LANDWEBER ITERATION; ALGORITHM;

D O I：

10.1088/1361-6420/aa7ac7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We perform a convergence analysis of a two-point gradient method which is based on Landweber iteration and on Nesterov's acceleration scheme. Additionally, we show the usefulness of this method via two numerical example problems based on a nonlinear Hammerstein operator and on the nonlinear inverse problem of single photon emission computed tomography.

引用

页数：30

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