A discrepancy principle for Tikhonov regularization with approximately specified data

  • Many discrepancy principles are known for choosing the parameter \(\alpha\) in the regularized operator equation \((T^*T+ \alpha I)x_\alpha^\delta = T^*y^\delta\), \(||y-y^d||\leq \delta\), in order to approximate the minimal norm least-squares solution of the operator equation \(Tx=y\). In this paper we consider a class of discrepancy principles for choosing the regularization parameter when \(T^*T\) and \(T^*y^\delta\) are approximated by \(A_n\) and \(z_n^\delta\) respectively with \(A_n\) not necessarily self - adjoint. Thisprocedure generalizes the work of Engl and Neubauer (1985),and particular cases of the results are applicable to the regularized projection method as well as to a degenerate kernel method considered by Groetsch (1990).

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Author:M. Thamban Nair, Eberhard Schock
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7231
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Source:Annales Polonici Mathematici
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification (mathematics):45-XX INTEGRAL EQUATIONS / 45Lxx Theoretical approximation of solutions (For numerical analysis, see 65Rxx) / 45L05 Theoretical approximation of solutions (For numerical analysis, see 65Rxx)
65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J20 Improperly posed problems; regularization
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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