The necessary and sufficient conditions for the approximations of linear ill-posed problems in a Hilbert space to converge

The weakest operational topology is derived, guaranteeing the convergence of permutations of solutions obtained by Tikhonov's regularizations method and the discrepancy method of linearized ill-posed problems in Hilbert spaces. Conditions are also derived for the systems of subspaces and operat...

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Bibliographic Details
Published in:U.S.S.R. computational mathematics and mathematical physics 1984, Vol.24 (3), p.5-9
Main Authors: Danilin, A.P., Tanana, V.P.
Format: Article
Language:English
Online Access:Get full text
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Summary:The weakest operational topology is derived, guaranteeing the convergence of permutations of solutions obtained by Tikhonov's regularizations method and the discrepancy method of linearized ill-posed problems in Hilbert spaces. Conditions are also derived for the systems of subspaces and operators which are necessary and sufficient for the approximations of the perturbations considered to converge.
ISSN:0041-5553
DOI:10.1016/0041-5553(84)90036-3