 Regularization of an inverse problem

A regularization is a family of bounded approximate inverses $R_{\alpha }$ together with a parameter rule $\alpha (\delta )$ such that $R_{\alpha (\delta )}{f}^{\delta }\to A^{†}f$ whenever $\Vert f^{\delta }-f\Vert \le \delta$ and $f$ lies in the domain of the Moore--Penrose inverse.