Abstract:
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.
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