## 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).

Author: M. Thamban Nair, Eberhard Schock urn:nbn:de:hbz:386-kluedo-7231 Preprint English 1999 1999 Technische Universität Kaiserslautern 2000/04/03 Annales Polonici Mathematici Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 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 Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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