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Iteratively solving linear inverse problems under general convex constraints. (English) Zbl 1123.65044
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.

MSC:
65J10 Numerical solutions to equations with linear operators (do not use 65Fxx)
65J22 Numerical solution to inverse problems in abstract spaces
47A50 Equations and inequalities involving linear operators, with vector unknowns
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