Regularization in Banach spaces — convergence rates by approximative source conditions : Journal of Inverse and Ill-posed Problems

www.degruyter.com uses cookies, tags, and tracking settings to store information that help give you the very best browsing experience.
To understand more about cookies, tags, and tracking, see our Privacy Statement
I accept all cookies for the De Gruyter Online site

Jump to ContentJump to Main Navigation

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


IMPACT FACTOR increased in 2014: 0.880
Rank 74 out of 310 in category Mathematics and 113 out of 255 in Applied Mathematics in the 2014 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2014: 0.516
Source Normalized Impact per Paper (SNIP) 2014: 1.430
Impact per Publication (IPP) 2014: 0.613

Mathematical Citation Quotient (MCQ) 2014: 0.51

VolumeIssuePage

Issues

Regularization in Banach spaces — convergence rates by approximative source conditions

T. Hein1

1Technische Universität Chemnitz, Fakultät für Mathematik, D-09107 Chemnitz, Deutschland. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 1, Pages 27–41, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.004, February 2009

Publication History

Received:
2008-07-25
Published Online:
2009-02-04

Abstract

In this paper we deal with convergence rates for a Tikhonov regularization approach for linear and nonlinear ill-posed problems in Banach spaces. Here, we deal with so-called distance functions which quantify the violation of a given reference source condition. With the aid of these functions we present error bounds and convergence rates for regularized solutions of linear and nonlinear problems when the reference source condition is violated. Introducing this topic for linear problems we extend the theory also to nonlinear problems. Finally an a-posteriori choice of the regularization parameter is suggested yielding the optimal convergence rate.

Key words.: Ill-posed problem; regularization; Banach space; distance function; convergence rates

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
T. Hein
Mathematical Modelling and Analysis, 2009, Volume 14, Number 4, Page 451
[2]
Torsten Hein and Kamil S. Kazimierski
Numerical Functional Analysis and Optimization, 2010, Volume 31, Number 10, Page 1158

Comments (0)

Please log in or register to comment.