Discrepancy principle for DSM

A. G. Ramm

Let $Ay=f$, $A$ is a linear operator in a Hilbert space $H$, $y\perp N(A):=\{u:Au=0\}$, $R(A):=\{h:h=Au,u\in D(A)\}$ is not closed, $\Vert f_{\delta }-f\Vert \le \delta$. Given $f_{\delta }$, one wants to cons…