Optimal order results for a class of regularization methods using unbounded operators

Integral Equations and Operator Theory

Volumn 44, Issue 1, 2002, Pages 79-92

  Nair, M Thamban ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036435928     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01197862     Document Type: Article

References (16)

1. J. Baumeister, Stable Solution of Inverse Problems, Friedr. Viewweg & Sohn, Braunsweig, Wiesbaden, Germany, 1987.
2. H.W. Engl, Regularization methods for the stable solution of inverse problems, Surveys Math. Indust. 3 (1993), 71-143.
3. H.W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Kluwer, Dordrecht, 1996.
4. C.W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Boston - London - Melbourne: Pitman Pub. 1984.
5. C.W. Groetsch, Inverse Problems in Mathematical Sciences, Braunschweg - Wiesbaden: Vieweg 1993.
6. M. Hanke, Regularization with differential operators: An alternative approach, Numer. Funct. Anal. Optim. 13 (1992), 523-540.
7. S.G. Krein and P.M. Petunin, Scales of Banach spaces, Russian Math. Surveys 21 (1966), 85-160.
8. A.K. Louis, Inverse und Schlecht Gestellte Probleme, B.G.Teubner, Stuttgart, 1989.
9. B.A. Mair, Tikhonov regularization for finitely and infinitely smoothing operators, SIAM J. Math. Anal. 25 (1994), 135-147.
10. C.A. Micchelli and T.J. Rivlin, A survey of optimal recovery. In: Optimal Estimation in Approximation Theory (eds.: C.A. Micchelli and T.J. Rivlin), Plenum Press, New York, 1977, pp. 1-53.
11. V.A. Morozov, Methods for Solving Incorrectly Posed Problems, New York et al., Springer - Verlag 1986.
12. M.T. Nair, M. Hegland, M. and R.S. Anderssen, The trade-off between regularity and stability in Tikhonov regularization, Mathematics of Computation 66 (1997), 193-206.
13. M.T. Nair, On Morozov's method for Tikhonov regularization as an optimal order yielding algorithm, Zeit. Anal. und ihre Anwend. 18 (1999), 37-46.
14. U. Tautenhahn, Error estimates for regularization methods in Hilbert scales, SEAM J. Numer. Anal. 33 (1996), 2120-2130.
15. G.M. Vainikko, The critical level of discrepancy in regularization methods, U.S.S.R. Comput. Math. and Math. Physics., 23 (1983), 1-9.
16. G.M. Vainikko, On the optimality of methods for ill-posed problems, Zeit. Anal. und ihre Anwend. 6 (1987), 351-362.