The minimality properties of Chebyshev polynomials and their lacunary series

Mason, J.C. (2005) The minimality properties of Chebyshev polynomials and their lacunary series. Numerical Algorithms, 38 (1). pp. 61-78. ISSN 1017-1398

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Abstract

By considering four kinds of Chebyshev polynomials, an extended set of (real) results are given for Chebyshev polynomial minimality in suitably weighted Hölder norms on [–1,1], as well as (L ) minimax properties, and best L 1 sufficiency requirements based on Chebyshev interpolation. Finally we establish best L p , L and L 1 approximation by partial sums of lacunary Chebyshev series of the form i=0 a i b i(x) where n (x) is a Chebyshev polynomial and b is an odd integer 3. A complete set of proofs is provided

Item Type:	Article
Subjects:	T Technology > T Technology (General) Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Schools:	School of Computing and Engineering
Depositing User:	Briony Heyhoe
Date Deposited:	22 Aug 2008 14:13
Last Modified:	22 Aug 2008 14:13
URI:	http://eprints.hud.ac.uk/id/eprint/1611

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