Geodesic
The Lagrange principle and finite-dimensional approximations in the optimal inverse problem for linear operators
Numerical methods and programming, Tome 7 (2006) no. 4, pp. 323-336

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This paper is devoted to the Lagrange principle for optimal recovery in the problem of solving operator equations. Some optimal recovery problems and a more general problem are formulated. The relation between the problem in infinite-dimensional space and its analogue in finite-dimensional space is studied. A theorem on common optimal recovery methods for the problems in infinite-dimensional space and in finite-dimensional space is proved. The problem in infinite-dimensional space is approximated by problems in finite-dimensional spaces. A new optimal method for the problem of solving operator equations in finite-dimensional space is described. This problem is considered as a system of linear algebraic equations with a priori information on its solution.
Keywords: optimal recovery, inverse problems on compact sets, finite-dimensional approximation, Lagrange principle, operator equations. 
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     author = {A. V. Bayev},
     title = {The {Lagrange} principle and finite-dimensional approximations in the optimal inverse problem for linear operators},
     journal = {Numerical methods and programming},
     pages = {323--336},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2006_7_4_a3/}
}
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A. V. Bayev. The Lagrange principle and finite-dimensional approximations in the optimal inverse problem for linear operators. Numerical methods and programming, Tome 7 (2006) no. 4, pp. 323-336. http://geodesic.mathdoc.fr/item/VMP_2006_7_4_a3/