Saturation of regularization methods for linear ill-posed problems in hilbert spaces

SIAM Journal on Numerical Analysis

Volumn 42, Issue 3, 2004, Pages 968-973

  Mathé, Peter ^a  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Ill posed problem; Regularization; Saturation

Indexed keywords

APPROXIMATION THEORY; LINEAR SYSTEMS; MATHEMATICAL MODELS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

HILLBERT SPACES; ILL-POSED PROBLEM; REGULARIZATION; SATURATION;

NUMERICAL METHODS;

EID: 21244441586     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142903420947     Document Type: Article

References (9)

1. R. BHATIA, Matrix Analysis, Springer-Verlag, New York, 1997.
2. H. W. ENGL, M. HANKE, AND A. NEUBAUER, Regularization of inverse problems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
3. M. HEGLAND, An optimal order regularization method which does not use additional smoothness assumptions, SIAM J. Numer. Anal., 29 (1992), pp. 1446-1461.
4. M. HEGLAND, Variable Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization, Appl. Anal., 59 (1995), pp. 207-223.
5. P. MATHÉ AND S. V. PEREVERZEV, Discretization strategy for linear ill-posed problems in variable Hilbert scales, Inverse Problems, 19 (2003), pp. 1263-1277.
6. P. MATHÉ AND S. V. PEREVERZEV, Geometry of linear ill-posed problems in variable Hilbert scales, Inverse Problems, 19 (2003), pp. 789-803.
7. A. NEUBAUER, On converse and saturation results for regularization methods, in Beiträge zur angewandten Analysis und Informatik, Shaker, Aachen, Germany, 1994, pp. 262-270.
8. A. NEUBAUER, On converse and saturation results for Tikhonov regularization of linear ill-posed problems, SIAM J. Numer. Anal., 34 (1997), pp. 517-527.
9. G. M. VAǏNIKKO AND A. YU. VERETENNIKOV, Iteratsionnye protsedury v nekorrektnykh zadachakh, Nauka, Moscow, 1986.