Applications of Integer Semi-Infinite Programing to the Integer Chebyshev Problem

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 programing 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.

Keywords:

• Integer Chebyshev problem
• semi-infinite programing

Mathematics Subject Classification:

• Primary 11C08
• 30C10
• 90C34

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research of K. G. Hare was supported by NSERC Grant 2014-03154. Research of P. W. Hodges was supported by NSERC Grant 2014-03154 and the President’s Research Award, Faculty of Mathematics, University of Waterloo.