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

Many discrepancy principles are known for choosing the parameter α in the regularized operator equation $(T*T+\alpha I){x}_{\alpha}^{\delta}=T*{y}^{\delta}$, $|y-{y}^{\delta}|\le \delta $, 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 $T*{y}^{\delta}$ are approximated by Aₙ and $z{\u2099}^{\delta}$ 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...