On the ill-posedness and regularization of third-kind integral equations : Journal of Inverse and Ill-posed Problems jiip Jump to ContentJump to Main Navigation
Show Summary Details

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


IMPACT FACTOR increased in 2015: 0.987
Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 0.583
Source Normalized Impact per Paper (SNIP) 2015: 1.106
Impact per Publication (IPP) 2015: 0.712

Mathematical Citation Quotient (MCQ) 2015: 0.43

249,00 € / $374.00 / £187.00*

Online
ISSN
1569-3945
See all formats and pricing
Select Volume and Issue
Loading journal volume and issue information...

30,00 € / $42.00 / £23.00

Get Access to Full Text

On the ill-posedness and regularization of third-kind integral equations

B. Büchler1

1Department of Mathematics, University of Kaiserslautern, PO Box 3049, D-67653 Kaiserslautern, Germany. Email:

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 15, Issue 4, Pages 329–346, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2007.018, June 2007

Publication History

Published Online:
2007-06-27

Linear integral equations of the third kind usually lead to ill-posed inverse problems if the normed solution space X and the normed data space Y are required to be equal. In the present paper we develop a two-step regularization method—called RPMO method—to regularize such inverse problems. This method does not require Hilbert space properties. Convergence results are presented indicating that there is no general theoretical upper bound less than one for the convergence rates if the corresponding exact data solutions are sufficiently smooth. Moreover, we illustrate the RPMO method by applying its discretized version to an implicit linear boundary value problem which can be transformed into an equivalent third-kind integral equation.

Key Words: Ill-posed problems,; regularization methods,; linear integral equations,; boundary value problems,; compactly disturbed multiplication operators.

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]
Paolo Capelli, Francesca Mariani, Maria Cristina Recchioni, Fabio Spinelli, and Francesco Zirilli
Inverse Problems in Science and Engineering, 2010, Volume 18, Number 1, Page 83

Comments (0)

Please log in or register to comment.