Convergence rates for Tikhonov regularization based on range inclusions

Inverse Problems

Volumn 21, Issue 3, 2005, Pages 805-820

  Hofmann, Bernd ^a   Yamamoto, Masahiro ^b  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; FUNCTIONS; INCLUSIONS; INVERSE PROBLEMS; LINEAR SYSTEMS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THERMAL EFFECTS;

CONVERGENCE RATES; HIBERT SPACES; RANGE INCLUSIONS; TIKHOV REGULARIZATION;

CONVERGENCE OF NUMERICAL METHODS;

EID: 18744408756     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/21/3/002     Document Type: Article

References (30)

1. Adams R A 1975 Sobolev Spaces (New York: Academic)
2. Ames K A and Straughan B 1997 Non-Standard and Improperly Posed Problems (San Diego, CA: Academic)
3. Baumeister J 1987 Stable Solution of Inverse Problems (Braunschweig: Vieweg)
4. Cheng J and Yamamoto M 2000 One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization Inverse Problems 16 L31-8
5. Colton D and Kress R 1992 Inverse Acoustic and Electromagnetic Scattering Theory (Berlin: Springer)
6. Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Dordrecht: Kluwer)
7. Fujiwara D 1967 Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order Proc. Japan Acad. 43 82-6
8. Gorenflo R and Yamamoto M 1999 Operator theoretic treatment of linear Abel integral equations of first kind Japan. J. Ind. Appl. Math. 16 137-61
9. Groetsch C W 1984 The Theory of Tikhonov Regularization for Fredholm Integral Equations of the First Kind (Boston, MA: Pitman)
10. Hegland M 1995 Variable Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization Appl. Anal. 59 207-23
11. Hofmann B 1986 Regularization for Applied Inverse and Ill-Posed Problems (Leipzig: Teubner)
12. Hofmann B 2004 The potential for ill-posedness of multiplication operators occurring in inverse problems Preprint 2004-17, Faculty of Mathematics, Chemnitz University of Technology, Chemnitz
13. Hofmann B and Fleischer G 1999 Stability rates for linear ill-posed problems with compact and non-compact operators J. Anal. Appl. 18 267-86
14. Hofmann B and Tautenhahn U 1997 On ill-posedness measures and space change in Sobolev scales J. Anal. Appl. 16 979-1000
15. Hohage T 2000 Regularization of exponentially ill-posed problems Numer. Funct. Anal. Optim. 21 439-64
16. Kirsch A 1996 An Introduction to the Mathematical Theory of Inverse Problems (New York: Springer)
17. Mair B A 1994 Tikhonov regularization for finitely and infinitely smoothing smoothing operators SIAM J. Math. Anal. 25 135-47
18. Mathé P and Pereverzev S V 2003 Geometry of linear ill-posed problems in variable Hilbert scales Inverse Problems 19 789-803
19. Mathé P and Pereverzev S V 2003 Discretization strategy for linear ill-posed problems in variable Hilbert scales Inverse Problems 19 1263-77
20. Natterer F 1984 Error bounds for Tikhonov regularization in Hilbert scales Appl. Anal. 18 29-37
21. Neubauer A 1987 Numerical realization of an optimal discrepancy principle for Tikhonov regularization in Hilbert scales Computing 39 43-55
22. Neubauer A 1988 When do Sobolev spaces form a Hilbert scale? Proc. Am. Math. Soc. 102 587-92
23. Russell D L 1973 A unified boundary controllability theory for hyperbolic and parabolic partial differential equations Stud. Appl. Math. 52 189-211
24. Tanabe H 1979 Equations of Evolution (London: Pitman)
25. Tautenhahn U 1998 Optimality for ill-posed problems under general source conditions Numer. Funct. Anal. Opt. 19 377-98
26. Tikhonov A N and Arsenin V Y 1977 Solutions of Ill-Posed Problems (New York: Wiley)
27. Tikhonov A N, Goncharsky A, Stepanov V and Yagola A 1995 Numerical Methods for the Solution of Ill-posed Problems (Dordrecht: Kluwer)
28. Vasin V V and Ageev A L 1995 Ill-Posed Problems with A Priori Information (Utrecht: VSP)
29. Yamamoto M 1995 Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method Inverse Problems 11 481-96
30. Yosida K 1980 Functional Analysis (New York: Springer)