Geodesic
Optimal recovery and finite-dimensional approximation in linear inverse problems
Sbornik. Mathematics, Tome 199 (2008) no. 12, pp. 1735-1750

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The paper considers applications of the Lagrange principle to optimal recovery in a linear inverse problem with a priori information about its solution and extends previous results of the author on optimal recovery and finite-dimensional approximation. A theorem on general optimal recovery methods for problems in finite- and infinite-dimensional spaces is established and the approximation of a problem in an infinite-dimensional space by problems in finite-dimensional spaces is investigated. Applications of the theory presented are illustrated by examples. Bibliography: 11 titles. 
@article{SM_2008_199_12_a0,
     author = {A. V. Bayev},
     title = {Optimal recovery and finite-dimensional approximation in linear inverse problems},
     journal = {Sbornik. Mathematics},
     pages = {1735--1750},
     publisher = {mathdoc},
     volume = {199},
     number = {12},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2008_199_12_a0/}
}
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A. V. Bayev. Optimal recovery and finite-dimensional approximation in linear inverse problems. Sbornik. Mathematics, Tome 199 (2008) no. 12, pp. 1735-1750. http://geodesic.mathdoc.fr/item/SM_2008_199_12_a0/