منابع مشابه
On 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...
متن کاملChebyshev Polynomials with Integer Coefficients
We study the asymptotic structure of polynomials with integer coef cients and smallest uniform norms on an interval of the real line Introducing methods of the weighted potential theory into this problem we improve the bounds for the multiplicities of some factors of the integer Chebyshev polynomials Introduction Let Pn C and Pn Z be the sets of algebraic polynomials of degree at most n respect...
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 Chebyshev Polynomials of Matrices
The mth Chebyshev polynomial of a square matrix A is the monic polynomial that minimizes the matrix 2-norm of p(A) over all monic polynomials p(z) of degree m. This polynomial is uniquely defined if m is less than the degree of the minimal polynomial of A. We study general properties of Chebyshev polynomials of matrices, which in some cases turn out to be generalizations of well known propertie...
متن کاملThe 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...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1997
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-97-00829-6