Inexact Newton regularization methods in Hilbert scales

We consider a class of inexact Newton regularization methods for solving nonlinear inverse problems in Hilbert scales. Under certain conditions we obtain the order optimal convergence rate result.

[1]  Error estimates of some Newton-type methods for solving nonlinear inverse problems in Hilbert scales , 2000 .

[2]  Andreas Rieder,et al.  On convergence rates of inexact Newton regularizations , 2001, Numerische Mathematik.

[3]  F. Natterer.  Error bounds for tikhonov regularization in hilbert scales , 1984 .

[4]  Martin Hanke,et al.  The regularizing Levenberg-Marquardt scheme is of optimal order , 2010 .

[5]  J. Köhler,et al.  Error bounds for regularized solutions of nonlinear ill-posed problems , 1995 .

[6]  R. Dembo,et al.  INEXACT NEWTON METHODS , 1982 .

[7]  Andreas Rieder,et al.  Towards a general convergence theory for inexact Newton regularizations , 2009, Numerische Mathematik.

[8]  Ulrich Tautenhahn,et al.  Error Estimates for Regularization Methods in Hilbert Scales , 1996 .

[9]  M. Hanke,et al.  A convergence analysis of the Landweber iteration for nonlinear ill-posed problems , 1995 .

[10]  Ulrich Tautenhahn,et al.  On a general regularization scheme for nonlinear ill-posed problems , 1997 .

[11]  A. Bakushinsky,et al.  Iterative Methods for Approximate Solution of Inverse Problems , 2005 .

[12]  Qinian Jin.  On a regularized Levenberg–Marquardt method for solving nonlinear inverse problems , 2010, Numerische Mathematik.

[13]  Alexander Ostermann,et al.  A convergence analysis of the exponential Euler iteration for nonlinear ill-posed problems , 2009 .

[14]  Andreas Rieder,et al.  On the regularization of nonlinear ill-posed problems via inexact Newton iterations , 1999 .

[15]  Ulrich Tautenhahn,et al.  On a general regularization scheme for nonlinear ill-posed problems: II. Regularization in Hilbert scales , 1998 .

[16]  Andreas Neubauer,et al.  On Landweber iteration for nonlinear ill-posed problems in Hilbert scales , 2000, Numerische Mathematik.

[17]  M. Hanke.  A regularizing Levenberg - Marquardt scheme, with applications to inverse groundwater filtration problems , 1997 .

[18]  H. Engl,et al.  Regularization of Inverse Problems , 1996 .