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).

Export metadata

  • Export Bibtex
  • Export RIS

Additional Services

Share in Twitter Search Google Scholar
Metadaten
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
Source:Annales Polonici Mathematici
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):45L05 Theoretical approximation of solutions (For numerical analysis, see 65Rxx)
65J20 Improperly posed problems; regularization

$Rev: 12793 $