A Modified Landweber Iteration for Solving Parameter Estimation Problems

Abstract. In this paper a convergence analysis for a modified Landweber iteration for the solution of nonlinear ill-posed problems is presented. A priori and a posteriori stopping criteria for terminating the iteration are compared. Some numerical results for the solution of a parameter estimation problem are presented.

[1]  Otmar Scherzer,et al.  Finite-dimensional approximation of tikhonov regularized solutions of non-linear ill-posed problems , 1990 .

[2]  H. Engl,et al.  Optimal a posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problems , 1993 .

[3]  Karl Kunisch,et al.  On Weakly Nonlinear Inverse Problems , 1996, SIAM J. Appl. Math..

[4]  A. Bakushinskii.  The problem of the convergence of the iteratively regularized Gauss-Newton method , 1992 .

[5]  Otmar Scherzer,et al.  Convergence Criteria of Iterative Methods Based on Landweber Iteration for Solving Nonlinear Problems , 1995 .

[6]  O. SCHERZER,et al.  On the Landweber iteration for nonlinear ill-posed problems , 1996 .

[7]  A. Bakushinskii,et al.  Ill-Posed Problems: Theory and Applications , 1994 .

[8]  Andreas Neubauer,et al.  Tikhonov regularisation for non-linear ill-posed problems: optimal convergence rates and finite-dimensional approximation , 1989 .

[9]  Curtis R. Vogel,et al.  Well posedness and convergence of some regularisation methods for non-linear ill posed problems , 1989 .

[10]  G. Rodrigue,et al.  A uniform approach to gradient methods for linear operator equations , 1975 .

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

[12]  A. Neubauer,et al.  On convergence rates for the Iteratively regularized Gauss-Newton method , 1997 .

[13]  Scherzer Otmar,et al.  A convergence analysis of a method of steepest descent and a two–step algorothm for nonlinear ill–posed problems , 1996 .

[14]  Andreas Neubauer,et al.  When do Sobolev spaces form a Hilbert scale , 1988 .