Geodesic
On the construction of families of optimal recovery methods for linear operators
Izvestiya. Mathematics , Tome 88 (2024) no. 1, pp. 92-113

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The paper proposes an approach for construction of families of optimal methods for the recovery of linear operators from inaccurately given information. The proposed method of construction is then applied to recover derivatives from inaccurately specified other derivatives in the multidimensional case and to recover solutions of the heat equation from inaccurately specified temperature distributions at some time instants.
Keywords: optimal recovery, linear operators, heat equation, difference equations. 
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     title = {On the construction of families of optimal recovery methods for linear operators},
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K. Yu. Osipenko. On the construction of families of optimal recovery methods for linear operators. Izvestiya. Mathematics , Tome 88 (2024) no. 1, pp. 92-113. http://geodesic.mathdoc.fr/item/IM2_2024_88_1_a5/