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Alternation theory in approximation by polynomials having bounded coefficients

Alternation theory in approximation by polynomials having bounded coefficients LetX be a compact subset of an interval [a, b] (a · b ≥ 0),fa continuous function defined onX, andK={p=Σ j=0 n α j xj:α j ≤a j ≤β j j=0,1, ...,n} the set of algebraic polynomials having bounded coefficients. The paper gives an alternating characterization theorem of a polynomial of best uniform approximation tof fromK, and a de La Vallée-Poussin theorem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Alternation theory in approximation by polynomials having bounded coefficients

Acta Mathematicae Applicatae Sinica , Volume 10 (3) – Jul 13, 2005

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Publisher
Springer Journals
Copyright
Copyright © 1994 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006857
Publisher site
See Article on Publisher Site

Abstract

LetX be a compact subset of an interval [a, b] (a · b ≥ 0),fa continuous function defined onX, andK={p=Σ j=0 n α j xj:α j ≤a j ≤β j j=0,1, ...,n} the set of algebraic polynomials having bounded coefficients. The paper gives an alternating characterization theorem of a polynomial of best uniform approximation tof fromK, and a de La Vallée-Poussin theorem.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

References