Using Lagrange principle for solving linear ill-posed problems with a priori information - Zhang, Ye.; Lukyanenko, D.V.; Yagola, A.G. (Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie), 2013)
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).