Publication Cover
Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 6
82
Views
0
CrossRef citations to date
0
Altmetric
Research Article

A modified Levenberg–Marquardt scheme for solving a class of parameter identification problems

ORCID Icon &
Pages 1080-1097 | Received 08 Feb 2022, Accepted 21 Jun 2023, Published online: 04 Jul 2023

References

  • Bakushinsky A, Goncharsky A. Ill-posed problems: theory and applications. Dordrecht: Kluwer, 1994.
  • Blaschke B, Neubauer A, Scherzer O. On convergence rates for the iteratively regularized Gauss–Newton method. IMA J Numer Anal. 1997;17:421–436. doi: 10.1093/imanum/17.3.421
  • Engl HW, Hanke M, Neubauer A. Regularization of inverse problems. Dordrecht: Kluwer; 1996.
  • Engl HW, Kunisch K, Neubauer A. Convergence rate for Tikhonov regularization of non-linear problems. Inverse Probl. 1989;5:523–540. doi: 10.1088/0266-5611/5/4/007
  • Hanke M. A regularizing Levenberg-Marquardt scheme with application to inverse ground water filteration problems. Inverse Probl. 1997;13:79–95. doi: 10.1088/0266-5611/13/1/007
  • Jose J, Rajan MP. A simplified Landweber iteration for solving nonlinear illposed Problems. Int J Appl Comput Math. 2017;3(Suppl1):S1001–S1018. doi: 10.1007/s40819-017-0395-4
  • Qi-Nian J. On a regularized Levenberg-Marquardt method for solving nonlinear inverse problems. Numer Math. 2010;115:229–259. doi: 10.1007/s00211-009-0275-x
  • Kaltenbacher B, Neubauer A, Scherzer O. Iterative regularization methods for Nonlinear ill-posed problems. New York: De Gruyter; 2008.
  • Pradeep D, Rajan MP. A simplified Gauss-Newton iterative scheme with an a posteriori parameter choice rule for solving nonlinear ill-posed problems. Int J Appl Comput Math. 2016;2(1):97–112. doi: 10.1007/s40819-015-0050-x
  • Pradeep D, Rajan MP. A regularized iterative scheme for solving nonlinear ill-posed problems. Numer Funct Anal Optim. 2015;37(3):342–362. doi: 10.1080/01630563.2015.1091013
  • Rajan MP. A modified Landweber iterative method for solving a class of parameter identification problems. J Inv Ill-Posed Probl. 2004;12(4):1–15.
  • Scherzer O. Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems. J Math Anal Appl. 1995;194:911–933. doi: 10.1006/jmaa.1995.1335
  • Hochbruck M, Hönig M. On the convergence of a regularizing Levenberg-Marquardt scheme for nonlinear ill-posed problems. Numerische Mathematik. 2010;115(1):71–79. doi: 10.1007/s00211-009-0268-9
  • Engl HW, Zou J. A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction. Inverse Probl. 2000;16:1907–1923. doi: 10.1088/0266-5611/16/6/319
  • Holder DS. Electrical impedance tomography: methods, history and applications. London: IOP Publishing Ltd; 2005.
  • Teschner E, Imhoff M, Leonhardt S. Electrical impedence tomography: the realisation of regional ventilation monitoring. Lubeck: Drägerwerk AG & Co KGaA; 2015.
  • Hauptmann A, Kolehmainen V, Minh Mach N, et al. Open 2D electrical impedance tomography data archive. arXiv:1704.01178v1 [physics.med-ph] (4 April 2017).
  • Choi MK, Harrach B, Seo JK. Regularizing a linearized EIT reconstruction method using a sensitivity based factorization method. Inverse Probl Sci Eng. 2014;22(7):1029–1044. doi: 10.1080/17415977.2013.850682
  • Bera TK, Nagaraju J. A MATLAB-based boundary data simulator for studying the resistivity reconstruction using neighbouring current pattern. J Med Eng. 2013;2013:193578. doi: 10.1155/2013/193578
  • Helfrich-Schkarbanenko A, Kreutzmann T. MATLAB software guide for 2D electrical impedance tomography, 2013.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.