Geodesic
Using Lagrange principle for solving linear ill-posed problems with a priori information
Numerical methods and programming, Tome 14 (2013) no. 4, pp. 468-482.

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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-NFSCa).
Keywords: ill-posed problems; regularization algorithms; optimal recovery; Lagrange principle; regularization parameter. 
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     author = {Y. Zhang and D. V. Luk'yanenko and A. G. Yagola},
     title = {Using {Lagrange} principle for solving linear ill-posed problems with a priori information},
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     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2013_14_4_a5/}
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Y. Zhang; D. V. Luk'yanenko; A. G. Yagola. Using Lagrange principle for solving linear ill-posed problems with a priori information. Numerical methods and programming, Tome 14 (2013) no. 4, pp. 468-482. http://geodesic.mathdoc.fr/item/VMP_2013_14_4_a5/