Results 11 to 20 of about 5,932 (309)
Brauer-Type Inclusion Sets of Zeros for Chebyshev Polynomial [PDF]
Mathematics, 2019 The generalized polynomials such as Chebyshev polynomial and Hermite polynomial are widely used in interpolations and numerical fittings and so on. Therefore, it is significant to study inclusion regions of the zeros for generalized polynomials.
Xiao Feng, Yaotang Li
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On the Coefficients and Zeros of a Polynomial [PDF]
Journal of Approximation Theory, 1999 In continuation of work by \textit{Q. I. Rahman} [Can. Math. Bull. 13, 541-542 (1970; Zbl 0205.37802)]\ and \textit{H. Alzer} [J. Approximation Theory 81, 421-424 (1995; Zbl 0837.30007)], the author offers two results on complex polynomials of the form \(p(z)=b_{0}+b_{1}z+b_{2}z^{2}+\cdots +b_{n}z^{n}\) with \(b_{0}=1.\) One states that the absolute ...
Shen, Dawei
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A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem [PDF]
, 1973 Elsner L. A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem. Numerische Mathematik. 1973;21(5):425-427.By using Gershgorin's theorem and the theorems on minimal Gershgorin disks a posteriori error bounds for the ...
Elsner, Ludwig
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On invariant zeros of linear systems of PDEs [PDF]
, 2006 In this paper we provide a behavioral framework in which to describe and extend the concept of linear dynamics introduced by Fliess, from the one dimensional (1D) to the multidimensional (nD) framework.We provide an alternative description of the ...
ZARIS, P +7 more
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New polynomial-based molecular descriptors with low degeneracy. [PDF]
PLoS ONE, 2010 In this paper, we introduce a novel graph polynomial called the 'information polynomial' of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set.
Matthias Dehmer +2 more
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On the relations between the zeros of a polynomial and its Mahler measure [PDF]
, 2021 International audienceIn this work, we are dealing with some properties relating the zeros of a polynomial and its Mahler measure. We provide estimates on the number of real zeros of a polynomial, lower bounds on the distance between the zeros of a ...
Rhin, Georges +2 more
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Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality [PDF]
, 2008 9 pages, no figures.-- MSC2000 code: 33C45.MR#: MR2431543 (2009g:41009)Zbl#: Zbl 1155.33006We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same $n ...
Díaz Mendoza, Carlos J. +3 more
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On the determination of the number of positive and negative polynomial zeros and their isolation
Open Mathematics, 2020 A novel method with two variations is proposed with which the number of positive and negative zeros of a polynomial with real coefficients and degree n can be restricted with significantly better determinacy than that provided by the Descartes rule of ...
Prodanov Emil M.
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SMIRNOV’S INEQUALITY FOR POLYNOMIALS HAVING ZEROS OUTSIDE THE UNIT DISC
Проблемы анализа, 2021 In 1887, the famous chemist D. I. Mendeleev posed the following problem: to estimate |𝑓 ′(𝑥)| for a real polynomial 𝑓 (𝑥), satisfying the condition |𝑓 (𝑥)| ≤ 𝑀 on [𝑎, 𝑏]. This question arose when Mendeleev was studying aqueous solutions.
E. G. Kompaneet, V. V. Starkov
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Equidistribution of Zeros of Polynomials [PDF]
The American Mathematical Monthly, 2019 A classical result of Erdos and Turan states that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small, then its zeros cluster near the unit circle and become equidistributed in angle. Using Fourier analysis we give a short and self-contained proof of this result.
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