Iterative methods for nonlinear ill-posed problems in Banach spaces: Convergence and applications to parameter identification problems

Inverse Problems

Volumn 25, Issue 6, 2009, Pages

  Kaltenbacher, Barbara ^a   Schöpfer, Frank ^b   Schuster, Thomas ^b  

^a UNIVERSITY OF STUTTGART   (Germany)

^b HELMUT SCHMIDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DISCREPANCY PRINCIPLE; ELLIPTIC PDES; GAUSS-NEWTON METHODS; ITERATIVE REGULARIZATION; NOISE LEVELS; NONLINEAR ILL-POSED PROBLEMS; PARAMETER IDENTIFICATION PROBLEMS; POSTERIORI; REGULARIZATION METHODS; REGULARIZATION PARAMETERS; STOPPING RULE; TWO PARAMETER;

BANACH SPACES; DYNAMIC LOADS; NEWTON-RAPHSON METHOD; TOPOLOGY;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 70350318924     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/25/6/065003     Document Type: Article

References (25)

1. Alber Y and Butnariu D 1997 Convergence of Bregman projection methods for solving consistent convex feasibility problems in reflexive Banach spaces J. Optim. Theory Appl. 92 33-61 (Pubitemid 127355475)
2. Bakushinsky A B 1992 The problem of the convergence of the iteratively regularized Gauss-Nnewton method Comput. Math. Math. Phys. 32 1353-9
3. Bakushinsky A B and Goncharsky A V 1994 Ill-posed Problems: Theory and Applications (Dordrecht: Kluwer)
4. Bakushinsky A B and Kokurin M 2004 Iterative Methods for Approximate solution of Inverse Problems (Dordrecht: Kluwer)
5. Bonesky T, Kazimierski K S, Maass P, Schöpfer F and Schuster T 2008 Minimization of Tikhonov functionals in Banach spaces Abstract Appl. Anal. doi:10.1155/2008/192679
6. Bregman L M 1967 The relaxation method for finding common points of convex sets and its application to the solution of problems in convex programming USSR Comput. Math. Math. Phys. 7 200-17
7. Butnariu D and Resmerita E 2006 Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces Abstract Appl. Anal. 84919 (39 pp)
8. Burger M and Osher S 2004 Convergence rates of convex variational regularization Inverse Problems 20 1411-21
9. Cioranescu I 1990 Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems (Dordrecht: Kluwer)
10. Engl H, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Dordrecht: Kluwer)
11. Engl H, Kunisch K and Neubauer A 1989 Convergence rates for Tikhonov regularization of nonlinear ill-posed problems Inverse Problems 5 523-40
12. Hanke M 1995 The minimal error conjugate gradient method is a regularization method Proc. Am. Math. Soc. 123 3487-97
13. Hanke M 1997 A regularization Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems Inverse Problems 13 79-95
14. 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
15. Hofmann B, Kaltenbacher B, Pöschl C and Scherzer O 2007 A convergence rates result in Banach spaces with non-smooth operators Inverse Problems 23 987-1010
16. Kaltenbacher (Blaschke) B, Neubauer A and Scherzer O 1997 On convergence rates for the iteratively regularized Gau -Newton method IMA J. Numer. Anal. 17 421-36
17. Kaltenbacher B and Neubauer A 2006 Convergence of projected iterative regularization methods for nonlinear problems with smooth solutions Inverse Problems 22 1105-19
18. Kaltenbacher B, Neubauer A and Scherzer O 2008 Iterative Regularization Methods for Nonlinear Ill-Posed Problems (Berlin: de Gruyter)
19. Louis A K 1989 Inverse und Schlecht Gestellte Probleme (Stuttgart: Teubner)
20. Resmerita E 2005 Regularization of ill-posed problems in Banach spaces: convergence rates Inverse Problems 21 1303-14
21. Rieder A 2001 On convergence rates of inexact Newton regularizations Numer. Math. 88 347-65 (Pubitemid 33577009)
22. Rieder A 2003 Keine Probleme Mit Inversen Problemen (Wiesbaden: Vieweg)
23. Schöpfer F, Louis A K and Schuster T 2006 Nonlinear iterative methods for linear ill-posed problems in Banach spaces Inverse Problems 22 311-29
24. Schöpfer F, Schuster T and Louis A K 2008 An iterative regularization method for the solution of the split feasibility problem in Banach spaces Inverse Problems 24 doi:10.1088/0266-5611/24/5/055008
25. Xu Z B and Roach G F 1991 Characteristic inequalities of uniformly convex and uniformly smooth spaces J. Math. Anal. Appl. 157 189-210