Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 6
Submit an article Journal homepage
130
Views
1
CrossRef citations to date
0
Altmetric
Articles

The analysis study on nonlinear iterative methods for inverse problems

Lingling DuFaculty of Science, Ningbo University, Ningbo, China.View further author information
,
Jing LiDepartment of Mathematics, Zhoukou Normal University, Zhoukou, China.View further author information
&
Jinping WangFaculty of Science, Ningbo University, Ningbo, China.Correspondence[email protected]
View further author information
Pages 925-935 | Received 14 Jan 2016, Accepted 14 Mar 2016, Published online: 04 Apr 2016

References

  • Hanke M, Neubauer A, Scherzer O. A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Numer. Math. 1995;72:21–37.
  • Bakushinsky AB. The problem of the convergence of the iteratively regularized Gauss--Newton method. Commput. Math. Math. Phys. 1992;32:1353–1359.
  • Hanke M. The minimal error conjugate gradient method is a regularization method. Proc. Am. Math. Soc. 1995;123:3487–3497.
  • Rieder A. On convergence rates of inexact Newton regularizations. Numer. Math. 2001;88:347–65.
  • Bonesky T, Kazimierski KS, Maass P, et al. Minimization of the Tikhonov functionals in Banach spaces. Abstract Appl. Anal. 2008;15:192679.
  • Hein T. On Tihkonov regularization in Banach spaces-optimal convergence rates results. Appl. Anal. 2009;88:653–667.
  • Schöpfer F, Schuster T, Louis AK. An iterative regularization method for the solution of the split feasibility problem in Banch spaces. Inverse Probl. 2008;24:055008.
  • Schöpfer F, Louis AK, Schuster T. Nonlinear iterative methods for linear ill-posed problems in Banach spaces. Inverse Probl. 2006;22:311–329.
  • Landweber L. An iteration formula for Fredholm integral equations of the first kind. Am. J. Math. 1951;73:615–24.
  • Plato R. On the discrepancy principle for iterative and parametric methods to solve linear ill-posed equations. Numer. Math. 1996;75:99–120.
  • Kokurin MY. Condition of sourcewise representability and estimates for convergence rate of methods for regularization of linear equations in Banach space. Russ. Math. 2001;45:49–57.
  • Xu Z-B, Roach GF. Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces. J. Math. Anal. Appl. 1991;157:189–210.
  • Hein T, Kazimierski KS. Modified Landweber iteration in Banach spaces-convergence and convergence rates. Numer. Funct. Anal. Optim. 2010;31:1158–1184.
  • Alber YI. Iterative regularization in Banach spaces. Russ. Math. 1986;30:1–8.
  • Alber YI, Kartsatos AG, Litsyn E. Iterative solution of unstable variational inequalities on approximately given sets. Abstract Appl. Anal. 1996;1:45–64.
  • Butnariu D, Iusem AN, Resmerita E. Total convexity for powers of the norm in uniformly convex Banach spaces. J. Convex Anal. 2000;7:319–334.

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.