Page "Tikhonov regularization" Paragraph 29

The optimal regularization parameter is usually unknown and often in practical problems is determined by an ad hoc method.

A possible approach relies on the Bayesian interpretation described above.

Other approaches include the discrepancy principle, cross-validation, L-curve method, restricted maximum likelihood and unbiased predictive risk estimator.

Grace Wahba proved that the optimal parameter, in the sense of leave-one-out cross-validation minimizes: