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## A discrepancy principle for Tikhonov regularization with approximately specified data

### Tom 69 / 1998

Annales Polonici Mathematici 69 (1998), 197-205 DOI: 10.4064/ap-69-3-197-205

#### Streszczenie

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).

#### Autorzy

• M. Thamban Nair
• Eberhard Schock

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