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

Content Provider	Springer Nature Link
Author	Nair, M. Thamban
Copyright Year	2002
Abstract	A class of regularization methods using unbounded regularizing operators is considered for obtaining stable approximate solutions for ill-posed operator equations. With an a posteriori as well as an a priori parameter choice strategy, it is shown that the method yields the optimal order. Error estimates have also been obtained under stronger assumptions on the generalized solution. The results of the paper unify and simplify many of the results available in the literature. For example, the optimal results of the paper include, as particular cases for Tikhonov regularization, the main result of Mair (1994) with an a priori parameter choice, and a result of Nair (1999) with an a posteriori parameter choice. Thus the observations of Mair (1994) on Tikhonov regularization of ill-posed problems involving finitely and infinitely smoothing operators is applicable to various other regularization procedures as well. Subsequent results on error estimates include, as special cases, an optimal result of Vainikko (1987) and also some recent results of Tautenhahn (1996) in the setting of Hilbert scales.
Ending Page	92
Page Count	14
Starting Page	79
File Format	PDF
ISSN	0378620X
e-ISSN	14208989
Journal	Integral Equations and Operator Theory
Issue Number	1
Volume Number	44
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2002-01-01
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems Integral equations Analysis Equations with linear operators Integral transforms Fredholm integral equations Equations and inequalities involving linear operators, with vector unknowns
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Analysis

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