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On polynomials of least deviation from zero

Mathematical Notes, 2010
Let \(\|\cdot\|_p\) be the norm in the space \(L_p[-1,1]\), \(1\leq p\leq \infty\). For \(q\leq q'\) let \(P_{q,q'}\) be the set of polynomials of degree \(q'\) whose coefficients of the term \(x^q\) are equal to \(1\). Let \(E(q,q')=\inf_{h\in P_{q,q'}}\|h\|_p\).
V A Yudin
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Bivariate Polynomials of Least Deviation from Zero

Canadian Journal of Mathematics, 2001
AbstractBivariate polynomials with a fixed leading term xmyn, which deviate least fromzero in the uniform or L2-norm on the unit disk D (resp. a triangle) are given explicitly. A similar problem in Lp, 1 ≤ p ≤ ∞, is studied on D in the set of products of linear polynomials.
Bojanov, Borislav D., Haussmann, Werner, Nikolov, Geno P.   +2 more
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Polynomials of Least Deviation from Zero

Mathematical Notes, 2005
The author studies the problem of approximating a homogeneous polynomial of degree \(n\) on the unit disk \(B\), i.e., a polynomial of the form \[ F(x,y) = \sum_{k=0}^n a_k x^k y^{n-k}, \] by algebraic polynomials of smaller degree, i.e., polynomials of the form \[ P(x,y) = \sum_{k+\ell \leq n-1} x^k y^{\ell}.
V A Yudin
exaly   +3 more sources

Polynomials of least deviation from zero in the L[−1, 1] metric with five fixed coefficients

Numerical Analysis and Applications, 2009
Let \(G\) be the set of polynomials of degree \(n+5\) with five fixed leading coefficients and let \(R_{n+5}(x)\) be a polynomial in \(G\) with the least possible \(L[-1,1]\)-norm. It is well-known that \(R_{n+5}(x)\) exists, is unique, and there are at least \(n+1\) points in the interval \((-1,1)\) where \(R_{n+5}(x)\) changes sign.
Gheit, V. E., Gheit, V. V.
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Blaschke products which have the least deviation from zero

Mathematical Notes, 1990
The following extremal problem is treated: find \[ \inf_{-1\leq x_ j\leq 1}\int^{b}_{a}| B(x,\{x_ j\})|^ qs(x)dx, \] where \(- 1\leq ...
K Yu Osipenko, Osipenko K Yu
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On trigonometric polynomials least deviating from zero

Doklady Mathematics, 2009
We give a solution of the problem about trigonometric polynomials with a given leading harmonic and least deviating from zero in measure; more precisely, with respect to the functional μ(fn) = mes {t ∈ [0, 2π]: |fn(t)| ≥ 1}. We give a solution of a related problem about the minimal value over compact sets (from the real line) of a given measure of ...
V. V. Arestov, A. S. Mendelev
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Polynomials of fixed sign that deviate least from zero in the spaces LP

Mathematical Notes of the Academy of Sciences of the USSR, 1985
It is proved that the finding of polynomials of constants signs of least deviation from zero in spaces \(L_ p\) with weight may be reduced to the similar problem on arbitrary polynomials but for other metric and other weight. This result generalizes one result of \textit{R. Bojanic} and \textit{R. De Vore} [Enseign. Math., II. Ser.
Babenko, V. F., Kofanov, V. A.
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Entire functions that deviate least from zero in the uniform and the integral metrics with a weight

St. Petersburg Mathematical Journal, 2015
Chebyshev and Bernstein's results about polynomials with the smallest deviation from zero in a weighted norm are extended to exponential-type entire functions. Functions with the smallest deviation from zero in some weighted spaces on the real axis, which generalize the Chebyshev polynomials of the first and the second kind, are constructed.
Gladkaya, A. V., Vinogradov, O. L.
openaire   +1 more source