Semi-iterative regularization in Hilbert scales

SIAM Journal on Numerical Analysis

Volumn 44, Issue 1, 2006, Pages 66-81

  Egger, Herbert ^a  

^a JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

Author keywords

Hilbert scales; Inverse problems; Regularization; Semi iterative methods

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; INVERSE PROBLEMS; ITERATIVE METHODS; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; THEOREM PROVING;

ITERATION NUMBERS; OPTIMAL CONVERGENCE RATES; REGULARIZATION; SEMI-ITERATIVE METHODS;

HILBERT SPACES;

EID: 33847662094     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040617285     Document Type: Article

References (19)

1. A. B. BAKUSHINSKII AND A. V. GONCHARSKII, Iterative Methods for Solving Ill-posed Problems, Nauka, Moscow, 1989 (in Russian).
2. H. BRAKHAGE, On ill-posed problems and the method of conjugate gradients, in Inverse and Ill-posed Problems, H. W. Engl and C. W. Groetsch, eds., Academic Press, New York, 1987, pp. 165-175.
3. H. EGGER AND A. NEUBAUER, Preconditioning Landweber iteration in Hilbert scales, Numer. Math., (2005), to appear.
4. H. W. ENGL, M. HANKE, AND A. NEUBAUER, Regularization of Inverse Problem, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
5. R. GORENFLO AND S. VESELLA, Abel integral equations: Analysis and applications, in Lecture Notes in Math. 1461, Springer-Verlag, Berlin, 1991.
6. C. W. GROETSCH, Generalized Inverses of Linear Operators, Marcel Dekker, New York, 1977.
7. C. W. GROETSCH, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Pitman, Boston, 1984.
8. M. HANKE, Accelerated Landweber iterations for the solution of ill-posed equations, Numer. Math., 60 (1991), pp. 341-373.
9. M. HANKE, A. NEUBAUER, AND O. SCHERZER, A convergence analysis of the Landweber iteration for nonlinear ill-posed problems, Numer. Math., 72 (1995), pp. 21-37.
10. B. KALTENBACHER, A. NEUBAUER, AND O. SCHERZER, Iterative Regularization Methods for Nonlinear Problems, in preparation.
11. S. G. KREIN AND J. I. PETUNIN, Scales of Banach spaces, Russian Math. Surveys, 21 (1966), pp. 85-160.
12. L. LANDWEBER, An iteration formula for Fredholm integral equations of the first kind, Amer. J. Math., 73 (1951), pp. 615-624.
13. J. L. LIONS AND E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications: Volume I, Springer, Berlin, 1972.
14. V. A. MOROZOV, On the solution of functional equations by the method of regularization, Soviet Math. Dokl., 7 (1966), pp. 414-417.
15. F. NATTERER, Error bounds for Tikhonov regularization in Hilbert scales, Appl. Anal., 18 (1984), pp. 29-37.
16. F. NATTERER, The Mathematics of Computerized Tomography, Teubner, Stuttgart, 1986.
17. A. NEUBAUER, Tikhonov regularization of nonlinear ill-posed problems in Hilbert scales, Appl. Anal., 46 (1992), pp. 59-72.
18. A. NEUBAUER, On Landweber iteration for nonlinear ill-posed problems in Hilbert scales, Numer. Math., 85 (2000), pp. 309-328.
19. U. TAUTENHAHN, Error estimates for regularization methods in Hilbert scales, SIAM J. Numer. Anal., 33 (1996), pp. 2120-2130.