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V. Titarenko, A. Yagola

Linear ill-posed problems on sets of convex functions on two-dimensional sets

Linear ill-posed problems written as the operator equation A = on sets of functions z convex on multi-dimensional sets Ω are considered in the paper. A regularizing algorithm z_η = R(A_h, u_δ, η), where ||A_h − A|| ≤ h, ||u_δ − || ≤ δ, η = (h,δ), obtained in the previous papers for line segments is generalized such that the approximate solution z_η tends to the exact one uniformly on some subsets of the domain Ω. The algorithms to estimate an error of finite dimensional approximation and to find a lower z^l and an upper z^u functions that bound all approximation solutions are provided.

Journal of Inverse and Ill-posed Problems, Walter de Gruyter

Print ISSN: 0928-0219
Volume: 14, 12/2006
Pages: 735 - 750

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