Generalized Gorshkov–Wirsing Polynomials and the Integer Chebyshev Problem

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Generalized 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 کامل

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 کامل

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 کامل

Chebyshev 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 کامل

The 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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Experimental Mathematics

سال: 2011

ISSN: 1058-6458,1944-950X

DOI: 10.1080/10586458.2011.564545