Geodesic
A discrepancy principle for Tikhonov regularization with approximately specified data
Annales Polonici Mathematici, Tome 69 (1998) no. 3, pp. 197-205.

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Many discrepancy principles are known for choosing the parameter α in the regularized operator equation $(T*T + αI)x_α^δ = T*y^δ$, $|y - y^δ| ≤ δ$, in order to approximate the minimal norm least-squares solution of the operator equation Tx = y. We consider a class of discrepancy principles for choosing the regularization parameter when T*T and $T*y^δ$ are approximated by Aₙ and $zₙ^δ$ respectively with Aₙ not necessarily self-adjoint. This procedure 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).
DOI : 10.4064/ap-69-3-197-205
Keywords: ill-posed problems, minimal norm least-squares solution, Moore-Penrose inverse, Tikhonov regularization, discrepancy principle, optimal rate

M. Thamban Nair 1 ; Eberhard Schock 1

1 
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M. Thamban Nair; Eberhard Schock. A discrepancy principle for Tikhonov regularization with approximately specified data. Annales Polonici Mathematici, Tome 69 (1998) no. 3, pp. 197-205. doi : 10.4064/ap-69-3-197-205. http://geodesic.mathdoc.fr/articles/10.4064/ap-69-3-197-205/

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