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Approximation of nonsmooth solutions of linear ill-posed problems. (English) Zbl 1130.47008
Maksimov, V. I. (ed.), Dynamical systems: modeling, optimization, and control. Transl. from the Russian. Moscow: Maik Nauka/Interperiodica, Pleiades Publishing/distrib. by Springer. Proc. Steklov Inst. Math. 2006, Suppl. 1, S247-S262 (2006); translation from Tr. Inst. Mat. Mekh. 12, No. 1, 64-77 (2006).
For the Tikhonov regularization of linear ill-posed operator equations, two families of stabilizers, containing Hölder space norms and norms of Sobolev spaces involving fractional derivatives, are suggested. The convergence of regularized solutions and their discrete approximations is established.
For the entire collection see [Zbl 1116.37003].

MSC:
47A52 Linear operators and ill-posed problems, regularization
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