Optimal Recovery and Extremum Theory

Optimal Recovery and Extremum Theory

In this paper optimal recovery problems of linear functionals on classes of smooth and analytic functions on the basis of linear information are considered from the general viewpoint of extremum theory. A general result about the connection of optimal recovery method with Lagrange multipliers of som...

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Veröffentlicht in:Computational methods and function theory 2003-06, Vol.2 (1), p.87-112
Hauptverfasser: Magaril-Il’yaev, Georgii G., Osipenko, Konstantin Yu, Tikhomirov, Vladimir M.
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Functionals
Lagrange multiplier
Recovery
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Zusammenfassung:In this paper optimal recovery problems of linear functionals on classes of smooth and analytic functions on the basis of linear information are considered from the general viewpoint of extremum theory. A general result about the connection of optimal recovery method with Lagrange multipliers of some convex extremal problem is applied to the analysis of classical recovery problems on the generalized Sobolev, Hardy, and Hardy-Sobolev classes.
ISSN:1617-9447
2195-3724
DOI:10.1007/BF03321011