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Expanding the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems

  • Ioannis K. Argyros
  • Yeol Je ChoEmail author
  • Santhosh George
  • Yi-bin Xiao
Original Paper
  • 9 Downloads

Abstract

We expand the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of the nonlinear ill-posed problem presented in Jin and Hou (Numer Math 83:139–159, 1999) by weakening the conditions needed in Jin and Hou [13]. Using a center-type Lipschitz condition instead of a Lipschitz-type condition used in Jin and Hou [13], Scherzer et al. (SIAM J Numer Anal 30:1796–1838, 1993), we obtain a tighter convergence analysis. Numerical examples are presented to show that our results apply but earlier ones do not apply to solve equations.

Keywords

Nonlinear ill-posed problems Tikhonov regularization Discrepancy principle 

Mathematics Subject Classification

65J20 65J15 47J06 

Notes

Acknowledgements

The research work was supported by the National Natural Science Foundation of China (11771067) and the Applied Basic Project of Sichuan Province (2019YJ0204).

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Copyright information

© The Royal Academy of Sciences, Madrid 2019

Authors and Affiliations

  • Ioannis K. Argyros
    • 1
  • Yeol Je Cho
    • 2
    • 3
    Email author
  • Santhosh George
    • 4
  • Yi-bin Xiao
    • 2
  1. 1.Department of Mathematicsal SciencesCameron UniversityLawtonUSA
  2. 2.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China
  3. 3.Department of Mathematics EducationGyeongsang National UniversityJinjuKorea
  4. 4.Department of Mathematical and Computational SciencesNational Institute of Technology KarnatakaMangaloreIndia

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