Alternating Chebyshev Approximation

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1973Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 178, page 95 (issn: 0002-9947,

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Authors: Dunham, Charles B.;

doi: 10.2307/1996691 , 10.1090/s0002-9947-1973-0318736-8

Alternating Chebyshev Approximation

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Abstract

An approximating family is called alternating if a best Chebyshev approximation is characterized by its error curve having a certain number of alternations. The convergence properties of such families are studied. A sufficient condition for the limit of best approximation on subsets to converge uniformly to the best approximation is given: it is shown that this is often (but not always) a necessary condition. A sufficient condition for the Chebyshev operator to be continuous is given: it is shown that this is often (but not always) a necessary condition.

Keywords

Best approximation, Chebyshev systems

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