The integer Chebyshev problem
نویسندگان
چکیده
منابع مشابه
The integer Chebyshev problem
We are concerned with the problem of minimizing the supremum norm on an interval of a nonzero polynomial of degree at most n with integer coefficients. This is an old and hard problem that cannot be exactly solved in any nontrivial cases. We examine the case of the interval [0, 1] in most detail. Here we improve the known bounds a small but interesting amount. This allows us to garner further i...
متن کاملThe Multivariate Integer Chebyshev Problem
The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in C. We study this problem on general sets, but devote special attention to product sets such as cube and polydisk. We also establish a multivariate analog of the Hilbert-Fekete upper bound for the integer Chebyshev constant, which depends on the dimens...
متن کاملMonic integer Chebyshev problem
We study the problem of minimizing the supremum norm by monic polynomials with integer coefficients. Let Mn(Z) denote the monic polynomials of degree n with integer coefficients. A monic integer Chebyshev polynomial Mn ∈ Mn(Z) satisfies ‖Mn‖E = inf Pn∈Mn(Z) ‖Pn‖E . and the monic integer Chebyshev constant is then defined by tM (E) := lim n→∞ ‖Mn‖ E . This is the obvious analogue of the more usu...
متن کاملGeneralized Gorshkov-Wirsing Polynomials and the Integer Chebyshev Problem
Interval LLL SIMPLEX HS Amoroso Lower # CP [-1, 1] 1/1.5314 1/1.5334 1/1.4772 1/1.4520 1/1.5417 8 [-1/2, 1/2] 1/2.3559 1/2.3619 1/2.1822 1/1.4520 1/2.3768 9 [-1/3, 1/3] 1/3.2522 1/3.2617 1/3.0000 1/1.3887 1/3.2842 7 [-2/3, 2/3] 1/1.8820 1/1.8883 1/1.7237 1/1.3887 1/1.9845 5 [-1/4, 1/4] 1/4.1921 1/4.2025 1/4.0000 1/1.1097 1/4.2260 6 [-3/4, 3/4] 1/1.7897 1/1.7935 1/1.7237 1/1.1097 1/1.9653 3 [-1/...
متن کاملOn integer Chebyshev polynomials
We are concerned with the problem of minimizing the supremum norm on [0, 1] 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 impr...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1996
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-96-00702-8