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Section B

Some convergence results of a modified asymptotical regularization gradient method for nonlinear ill-posed operator equation

, &
Pages 2811-2822 | Received 14 Mar 2008, Accepted 08 Feb 2009, Published online: 17 Jun 2010

References

  • Airapetyan , R. G. and Ramm , A. G. 2000 . “ Dynamical Systems and Discrete Methods for Solving Nonlinear Ill-Posed Problems ” . In Applied Mathematics Reviews , Vol. 1 , 491 – 536 . World Sci. Pub. Co .
  • R.G. Airapetyan, A.G. Ramm, and A.B. Smirnova, Continous Methods for Solving Nonlinear Ill-Posed Problems, Operator theory and its Application Vol. 25, Americal Mathematical Society, Fields Inst. Commun., Providence R.I., 2000, 111–137
  • Bakushinsky , A. B. 1998 . Iterative methods of gradient type for nonregular operator equations . Comput. Math. Math. Phys. , 38 : 1884 – 1887 .
  • Bakushinsky , A. B. and Kokurin , M. Y. 2004 . Iterative Methods for Approximate Soution of Inverse Problems , The Netherlands : Springer .
  • Bakushinsky , A. B. and Smirnova , A. 2005 . On application of generalized discrepancy principle to iterative methods for nonlinear ill-posed problems . Numer. Funtc. Anal. Optim. , 26 : 35 – 48 .
  • Engl , H. W. , Hanke , M. and Neubauer , A. 1996 . Regularization of Inverse Problems , Dordrecht : Kluwer .
  • Hanke , M. , Neubauer , A. and Scherzer , O. 1995 . A convergence analysis of the Landweber iteration for nonlinear ill-posed problems . Numer. Math. , 72 : 21 – 37 .
  • Khan , T. and Smirnova , A. 2005 . 1D inverse problem in diffusion based optical tomography using iteratively regularized Gauss-Newton algorithm . Appl. Math. Comput. , 161 : 149 – 170 .
  • Li , L. , Han , B. and Wang , W. 2006 . R–K type Landweber method for nonlinear ill-posed problems . J. Comput. Appl. Math. , 206 : 341 – 357 .
  • Ramm , A. G. 2007 . “ Dynamical Systems Method for Solving Operator Equations ” . Amsterdam : Elsevier .
  • Scherzer , O. 1998 . A Modified Landweber Iteration for Solving Parameter Estimation Problems . Appl. Math. Optim. , 38 : 45 – 68 .
  • Tautenhahn , U. 1994 . On the asymptotical regulariztion of nonlinear ill-posed problems . Inverse Problems , 10 : 1405 – 1418 .

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