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arXiv · 1804.05985

Applications of Integer and Semi-Infinite Programming to the Integer Chebyshev Problem

Kevin G. Hare·Philip W. Hodges
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Abstract

We consider the integer Chebyshev problem, that of minimizing the supremum norm over polynomials with integer coefficients on the interval $[0,1]$. We implement algorithms from semi-infinite programming and a branch and bound algorithm to improve on previous methods for finding integer Chebyshev polynomials of degree $n$. Using our new method, we found 16 new integer Chebyshev polynomials of degrees in the range 147 to 244.

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Kevin G. Hare, Philip W. Hodges. 2018-10-26. Applications of Integer and Semi-Infinite Programming to the Integer Chebyshev Problem. https://arxiv.org/abs/1804.05985

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