"Using Lagrange principle for solving linear ill-posed problems with a priori information"
Zhang Ye, Lukyanenko D.V., Yagola A.G.

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 11–01–00040, 12–01–00524 and 12–01–91153–NFSC_a).

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

Zhang Ye, e-mail: zhangye@physics.msu.ru;   Lukyanenko D.V., e-mail: lukyanenko@physics.msu.ru;   Yagola A.G., e-mail: yagola@physics.msu.ru – Moscow State University, Faculty of Physics; Leninskiye Gory, Moscow, 119992, Russia