Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces

被引：20

作者：

Albani, V. ^{[1
]}

Elbau, P. ^{[1
]}

de Hoop, M. V. ^{[2
,3
]}

Scherzer, O. ^{[1
,4
]}

机构：

[1] Univ Vienna, Computat Sci Ctr, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[2] Rice Univ, Dept Computat & Appl Math, Houston, TX USA

[3] Rice Univ, Dept Earth Sci, Houston, TX USA

[4] Johann Radon Inst Computat & Appl Math RICAM, Linz, Austria

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2016年 / 37卷 / 05期

基金：

奥地利科学基金会;

关键词：

Approximative source conditions; convergence rates; linear inverse problems; regularization; variational source conditions; TIKHONOV REGULARIZATION;

D O I：

10.1080/01630563.2016.1144070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection to approximative source conditions.

引用

页码：521 / 540

页数：20

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