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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
65J22 Numerical solution to inverse problems in abstract spaces
47A50 Equations and inequalities involving linear operators, with vector unknowns
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