Regularization of ill-posed problems with normally resolvable operators (Q1974733)

The authors consider the following minimization problem in Hilbert space \(U\): \[ \min\|u\|, \quad U\subset U_f, \quad U_f= \{u\in D: Au=f\}, \] where the operator \(A\) and an element \(f\) are given approximately, i.e. \(\|A_\eta- A\|\leq \eta\), \(\|f_\delta- f\|\leq \delta\), \(0< \eta\leq \eta^*< \infty\) and \(D\) a convex, closed set from \(U\). Regularization methods for these ill-posed problems are analyzed. These methods can be used to approximate a pseudosolution with a rate of error equal to that of the initial date \(\eta\) and \(\delta\).