On the regularizing properties of a full multigrid method for ill-posed problems

Inverse Problems

Volumn 17, Issue 4, 2001, Pages 767-788

  Kaltenbacher, Barbara ^b  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035419872     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/17/4/313     Document Type: Article

References (32)

1. Bardos C, Brezis D and Brezis H 1973 Perturbations singulières et prolonguements maximaux d'opérateurs positives Arch. Rat. Mech. Anal. 53 69-100
2. Braess D and Hackbusch W 1983 A new convergence proof for the multigrid method including the V-cycle SIAM J. Numer. Anal. 20 967-75
3. Bramble J 1993 Multigrid Methods (Pitman Research Notes in Mathematics Series vol 294) (Harlow: Longman)
4. Bramble J H, Leyk Z and Pasciak J E 1994 The analysis of multigrid algorithms for pseudo-differential operators of order minus one Math. Comput. 63 461-78
5. Bramble J H and Pasciak J E 1993 New estimates for multigrid algorithms including the V-cycle Math. Comput. 60 447-71
6. Bramble J H, Pasciak J E, Wang J and Xu J 1991 Convergence estimates for multigrid algorithms without regularity assumptions Math. Comput. 57 23-45
7. Bramble J H, Pasciak J E and Xu J 1990 Parallel multilevel preconditioners Math. Comput. 55 1-22
8. Brandt A 1977 Multilevel adaptive solutions to boundary value problems Math. Comput. 31 333-90
9. [91 Ciarlet P C 1978 The Finite Element Method for Elliptic Problems (Amsterdam: North-Holland)
10. Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Dordrecht: Kluwer)
11. Engl H W and Neubauer A 1987 On projection methods for solving linear ill-posed problems Model Optimization in Exploration Geophysics ed A Vogel (Braunschweig: Vieweg) pp 73-92
12. Groetsch C W 1993 Inverse Problems in Mathematical Sciences (Braunschweig: Vieweg)
13. Groetsch C W and Neubauer A 1988 Convergence of a general projection method for an operator equation of the first kind Houston J. Math. 14 201-7
14. Haase G, Langer U, Meyer A and Nepomnyashikh S V 1994 Hierarchical extension operators and local multigrid methods in domain decomposition preconditioners East-West J. Numer. Math. 2 179-93
15. Hackbusch W 1985 Multi-Grid Methods and Applications (Berlin: Springer)
16. Hanke M 1997 A regularization Levenberg-Marquardt scheme, with applications to inverse ground-water filtration problems Inverse Problems 13 79-95
17. 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
18. Hanke M and Vogel C R 1999 Two-level preconditioners for regularized inverse problems I: Theory Numer. Math. 83 385-402
19. Kaltenbacher B 2000 A multi-grid method with a priori and a posteriori level choice for the regularization of nonlinear ill-posed problems SFB013-Report No 00-3 University of Linz
20. Kaltenbacher B 2000 Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems Inverse Problems 16 1523-39
21. Kaltenbacher B 2000 V-cycle convergence of some multigrid methods for ill-posed problems SFB013-Report University of Linz
22. Kaltenbacher B and Kaltenbacher M Identification of nonlinear B-H curves based on magnetic field computations and using multigrid preconditioners for ill-posed problems at press
23. King J T 1990 On the construction of preconditioners by subspace decomposition J. Comput. Appl. Math. 29 195-205
24. King J T 1992 Multilevel algorithms for ill-posed problems Numer. Math. 61 311-34
25. Louis A K 1989 Inverse und Schlecht Gestellte Probleme (Stuttgart: Teubner)
26. Morozov V A 1993 Regularization Methods for Ill-Posed Problems (Boca Raton, FL: CRC Press)
27. Natterer F 1977 Regularisierung schlecht gestellter Probleme durch Projektionsverfahren Numer. Math. 28 329-41
28. Natterer F 1986 The Mathematics of Computerized Tomography (Stuttgart: Teubner)
29. Rieder A 1997 A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization Numer. Math. 75 501-22
30. Tikhonov A N and Arsenin V A 1979 Methods for Solving Ill-Posed Problems (Moskow: Nauka)
31. Vainikko G and Hämarik U 1985 Projection methods and self-regularization in ill-posed problems Sov. Math. 29 1-20 (in Russian)
32. Vainikko G M and Veterennikov A Y 1986 Iteration Procedures in Ill-Posed Problems (Moscow: Nauka) (in Russian)