Iteratively solving linear inverse problems under general convex constraints (Q995437)

Let \(T\) be a bounded operator from a Hilbert space \({\mathcal H}\) into itself, with \(\| T \|<1\), and \(C\) a closed convex subset of \({\mathcal H}\). For solving linear operator equations \(Tf=h\) the iterative process \(f_{n+1}=(\text{Id}-P_{\alpha C})(f_n+T^*g-T^* T f_n)\), \(\alpha>0\) is proposed. The cases of bounded and unbounded \((T^* T)^{-1}\) are considered.