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Mathematics of Computation

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On Integer Chebyshev Polynomials

Authors: Laurent Habsieger and Bruno Salvy
Journal: Math. Comp. 66 (1997), 763-770
MSC (1991): Primary 11J54, 11-04, 41A10, 41-04
MathSciNet review: 1401941
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Abstract: We are concerned with the problem of minimizing the supremum norm on $\lbrack 0,1\rbrack $ of a nonzero polynomial of degree at most $n$ with integer coefficients. We use the structure of such polynomials to derive an efficient algorithm for computing them. We give a table of these polynomials for degree up to $75$ and use a value from this table to answer an open problem due to P. Borwein and T. Erdélyi and improve a lower bound due to Flammang et al.

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Additional Information

Laurent Habsieger
Affiliation: Laboratoire d’Algorithmique Arithmétique, CNRS UMR 9936, Université Bordeaux 1, 351 cours de la Libération, F-33405 Talence Cedex, France

Bruno Salvy
Affiliation: INRIA Rocquencourt, Domaine de Voluceau, B.P. 105, F-78153 Le Chesnay Cedex, France

Received by editor(s): October 18, 1995
Received by editor(s) in revised form: May 3, 1996
Article copyright: © Copyright 1997 American Mathematical Society