Economic discretization scheme for the nonstationary iterated Tikhonov method (Q995946)

The author considers the equation \(Ax=f\), \(f \in R(A)\), with a compact linear operator \(A: X \to X\) in a Hilbert space \(X\). Let \(f_{\delta} \in X\) be an available approximation to \(f\), \(\| f_{\delta}-f \| \leq \delta\). An adaptive discretization scheme is applied to the iterated Tikhonov regularization method \(x_0=0\), \(x_l=\alpha (A^* A+\alpha I)^{-1} x_{l-1}+(A^* A+\alpha I)^{-1} A^* f_{\delta}\).