Linear ill-posed problems with a priori information on the exact solution are considered. Using the method of extending compacts, the Lagrange principle and the optimal recovery theory, we propose a method for constructing an optimal regularization algorithm for solving linear ill-posed problems with sourcewise representable solutions and a method of calculating the corresponding optimal worst a posteriori error estimate of the proposed method. A numerical simulation of a heat equation is also considered. This work was partially supported by the Russian Foundation for Basic Research (projects 11òÀÓ01òÀÓ00040, 12òÀÓ01òÀÓ00524 and 12òÀÓ01òÀÓ91153òÀÓNFSC_a).

Keywords: ill-posed problems, regularization algorithms, optimal recovery, Lagrange principle, regularization parameter

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