Tikhonov regularization in Banach spaces - Improved convergence rates results

Inverse Problems

Volumn 25, Issue 3, 2009, Pages

  Hein, Torsten ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE RATES; DECAY RATE; DISTANCE FUNCTIONS; ERROR BOUND; IMPROVED CONVERGENCE; LINEAR ILL-POSED PROBLEMS; REFERENCE SOURCE; REGULARIZATION APPROACH; TIKHONOV REGULARIZATION;

BANACH SPACES; DECAY (ORGANIC);

TOPOLOGY;

EID: 70350333275     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/25/3/035002     Document Type: Article

References (20)

1. Bauer F and Hohage T 2005 A Lepskij-type stopping rule for regularized Newton methods Inverse Problems 21 1979-91
2. Burger M and Osher S 2004 Convergence rates of convex variational regularization Inverse Problems 20 1411-21
3. Cioranescu I 1990 Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems (Dordrecht: Kluwer)
4. Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Dordrecht: Kluwer)
5. Hein T 2009 Regularization of ill-posed problems in Banach spaces-approximative source conditions and convergence rates results J. Inv. Ill-Posed Problems 17 at press
6. Hein T 2008 Convergence rates for regularization of ill-posed problems in Banach spaces by approximate source conditions Inverse Problems 24 045007
7. Hofmann B 2006 Approximative source conditions in Tikhonov-Phillips regularization and consequences for inverse problems with multiplication operators Math. Methods Appl. Sci. 29 351-71
8. Hofmann B, Düvelmeyer D and Krumbiegel K 2006 Approximate source condition in Tikhonov regularization-new analytical results and some numerical studies Math. Mod. Anal. 11 41-56
9. 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
10. Hofmann B, Düvelmeyer D and Yamamoto M 2007 Range inclusions and approximative source conditions with general benchmark functions Numer. Funct. Anal. Optim. 28 1245-61
11. Hofmann B and Mathé P 2007 Analysis of profile functions for general linear regularization methods SIAM J. Numer. Anal. 45 1122-41
12. Lepskij O V 1990 A problem of adaptive estimation in Gaussian withe noise Teor. Veroyatn. Primen. 35 459-70
13. Mathé P 2006 The Lepskij principle revisited Inverse Problems 22 L11-5
14. Resmerita E 2005 Regularization of ill-posed problems in Banach spaces: convergence rates Inverse Problems 21 1303-14
15. Resmerita E and Scherzer O 2006 Error estimates for non-quadratic regularization and the relation to enhancement Inverse Problems 22 801-14
16. 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
17. Seidman T I and Vogel C R 1989 Well posedness and convergence of some regularization methods for non-linear ill-posed problems Inverse Problems 5 227-38
18. Werner D 1997 Funktionalanalysis (in German) (Berlin: Springer)
19. Xu Z-B and Roach G F 1991 Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces J. Math. Anal. Appl. 157 189-210
20. Zeidler E 1985 Nonlinear Functional Analysis and its Applications III (New York: Springer)