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An iterative method to compute minimum norm solutions of ill-posed problems in Hilbert spaces

  • Meisam Jozi
  • Saeed KarimiEmail author
  • Davod Khojasteh Salkuyeh
Article
  • 7 Downloads

Abstract

We study an algorithm to compute minimum norm solution of ill-posed problems in Hilbert spaces and investigate its regularizing properties with discrepancy principle stopping rule. This algorithm results from straightly applying the LSQR method to the main problem before discretizing. In fact, the proposed algorithm obtains a sequence of approximate solutions of the original problem. In order to test the new algorithm, it is implemented to solve system of linear integral equations of the first kind and some examples are given. Moreover, we compare the presented algorithm with the Tikhonov regularization method to compute the least norm solution when there are more than one solution.

Keywords

Ill-posed problem First kind equations Regularization method \(\mathcal {LS}\)-algorithm Minimum norm 

Mathematics Subject Classification

45N05 45Q05 45P05 45A05 47B38 47B34 

Notes

Acknowledgements

The authors would like to thank the referee for his/her helpful comments and suggestions.

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPersian Gulf UniversityBushehrIran
  2. 2.Faculty of Mathematical SciencesUniversity of GuilanRashtIran

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