Results 241 to 250 of about 1,450,713 (273)

Polynomials of least deviation from zero

Proceedings of the Steklov Institute of Mathematics, 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}.
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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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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 \(E(q,q')=\inf_{h\in P_{q,q'}}\|h\|_p\).
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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 of the Academy of Sciences of the USSR, 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 ...
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EXPONENTIAL POLYNOMIALS OF LEAST DEVIATION FROM ZERO AND OPTIMAL QUADRATURE FORMULAS

Mathematics of the USSR-Sbornik, 1984
Translation from Mat. Sb., Nov. Ser. 120(162), No.2, 273-285 (Russian) (1983; Zbl 0529.41028).
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Dealing with zero response data from contingent valuation surveys: application of least absolute deviations estimator

Applied Economics Letters, 2000
Data on willingness-to-pay (WTP) collected from contingent valuation surveys are usuallycensoredat zero. Insuch cases, ordinary least squares estimationof the WTP equation produces inconsistent parameter estimates. The maximum likelihood estimation of the Tobit model, which is widely used in this case, is not robust to heteroscedasticity and non-normal
Seung-Hoon Yoo, Seung-Jun Kwak, Tai-Yoo Kim   +2 more
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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.
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Polynomials Least Deviating from Zero on a Square of the Complex Plane

Proceedings of the Steklov Institute of Mathematics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Algebraic polynomials least deviating from zero in measure on a segment

Ukrainian Mathematical Journal, 2010
Summary: We investigate the problem of algebraic polynomials with given leading coefficients that deviate least from zero on the segment \([-1,1]\) with respect to a measure, or, more precisely, with respect to the functional \(\mu(f) =\text{mes}\{x\in [-1, 1]: | f (x)| \geq 1\}\).
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