On Optimal Recovery of Heat Equation Solutionsстатья

Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.

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[1] Magaril-Il'yaev G. G., Osipenko K. Y., Tikhomirov V. M. On optimal recovery of heat equation solutions // Approximation Theory: A volume dedicated to Borislav Bojanov (D.K. Dimitrov, G. Nikolov, and R. Ulechev, Eds.). — Marin Drinov Academic Publishin House Sofia, 2004. — P. 163–175. In this paper, we consider some optimal recovery problems which are representatives of a vast number of problems in numerical analysis. We focus on the so called cleaning phenomenon, where only a part of the given information is used for the construction of an optimal recovery method in the uniform norm. There are a lot of results concerning the optimal recovery of linear functionals (see, for example, [1]–[5] and the references therein). However, the problems of optimal recovery of linear operators are not studied that extensively (see [6]–[8]). Here, we present some results about op- timal recovery of solutions to differential equations and illustrate our approach in the case of solutions to the heat equation u_t = u_{xx}.

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