Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year

IMPACT FACTOR 2016: 0.783
5-year IMPACT FACTOR: 0.792

CiteScore 2016: 0.80

SCImago Journal Rank (SJR) 2016: 0.589
Source Normalized Impact per Paper (SNIP) 2016: 1.125

Mathematical Citation Quotient (MCQ) 2015: 0.43

See all formats and pricing
More options …
Volume 19, Issue 1 (Jan 2011)


Why a minimizer of the Tikhonov functional is closer to the exact solution than the first guess

Michael V. Klibanov / Anatoly B. Bakushinsky
  • Institute for System Analysis of The Russian Academy of Science, Prospect 60 letya Oktyabrya 9, 117312, Moscow, Russia.
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Larisa Beilina
  • Department of Mathematical Sciences, Chalmers University and Gothenburg University, SE-42196, Gothenburg, Sweden.
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2011-05-02 | DOI: https://doi.org/10.1515/jiip.2011.024


Suppose that a uniqueness theorem is valid for an ill-posed problem. It is shown then that the distance between the exact solution and terms of a minimizing sequence of the Tikhonov functional is less than the distance between the exact solution and the first guess. Unlike the classical case when the regularization parameter tends to zero, only a single value of this parameter is used. Indeed, the latter is always the case in computations. Next, this result is applied to a specific coefficient inverse problem. A uniqueness theorem for this problem is based on the method of Carleman estimates. In particular, the importance of obtaining an accurate first approximation for the correct solution follows from Theorems 7 and 8. The latter points towards the importance of the development of globally convergent numerical methods as opposed to conventional locally convergent ones. A numerical example is presented.

Keywords.: Uniqueness theorem; Tikhonov functional; a single value of the level of error

About the article

Received: 2010-09-28

Published Online: 2011-05-02

Published in Print: 2011-05-01

Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2011.024.

Export Citation

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.

Anders Eriksson, Larisa Beilina, and Truls Martin Larsen
Journal of Mathematics in Industry, 2017, Volume 7, Number 1
Larisa Beilina and Samar Hosseinzadegan
Applications of Mathematics, 2016, Volume 61, Number 3, Page 253
Larisa Beilina, Nguyen Trung Thành, Michael V. Klibanov, and John Bondestam Malmberg
Journal of Computational and Applied Mathematics, 2015, Volume 289, Page 371
A. Timonov
Inverse Problems in Science and Engineering, 2014, Volume 22, Number 8, Page 1329
Larisa Beilina and Michael V. Klibanov
Applicable Analysis, 2014, Volume 93, Number 2, Page 223
A. V. Kuzhuget, L. Beilina, and M. V. Klibanov
Journal of Mathematical Sciences, 2012, Volume 181, Number 2, Page 126
Larisa Beilina and Michael V. Klibanov
Complex Variables and Elliptic Equations, 2012, Volume 57, Number 2-4, Page 277
Jingzhi Li, Jianli Xie, and Jun Zou
Inverse Problems, 2011, Volume 27, Number 7, Page 075009

Comments (0)

Please log in or register to comment.
Log in