This article is cited in 3 papers

Вычислительные методы и приложения

The Lagrange principle and finite-dimensional approximations in the optimal inverse problem for linear operators

A. V. Bayev

Lomonosov Moscow State University, Faculty of Physics

Abstract: 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.

UDC: 517.983