Abstract
One investigates the error of the projection methods in solving the problem regarding the shortest distance from a point to a closed convex set M in a Hilbert space H. One introduces the concept of equipotential convexity of a set M and one gives an estimate of the error of the mentioned methods in terms of the best approximation by elements of the intersection X ∩ M, where X is the projection plane in H. One gives an example which shows that, in general, without the condition of equipotential convexity such an estimate cannot be obtained.
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Literature cited
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituts im. V. A. Steklova AN SSSR, Vol. 102, pp. 5–18, 1980.
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Dem'yanovich, Y.K. Error estimate of the projection methods in the problem of best approximation. J Math Sci 22, 1171–1178 (1983). https://doi.org/10.1007/BF01460268
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DOI: https://doi.org/10.1007/BF01460268