Results 31 to 40 of about 5,932 (309)

On the Zeros of Polynomials

Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1977
1. Govil and Rahman [1, Theorem 1] have proved the fol- lowing theorem.n Theorem A. Let p (z) = £ aj^ k“0 z’^ ( 0) be a polynomiai ofdegree n with complex coefficients such that for some a>«-1 I a^ •11-2 a' I »ol-Then p (z) has ali its zeros in |z Kj, where Kj is the greatest positive root of the trinomial equation K"+ı - 2K" + 1 =
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Imaginary part bounds on polynomial zeros [PDF]

, 1982
Bounds for the imaginary parts of the zeros of a polynomial are given by the generalization of [6] and by the improvement of [3].
László, Lajos, Lajos László
core   +1 more source

A Maple Implementation for Deterministically Certifying Isolated Simple Zeros of Over-Determined Polynomial Systems with Interval Arithmetic and Its Applications

AppliedMath
This paper presents a Maple implementation of an interval verification method for identifying isolated simple zeros in square polynomial systems. Compared to the known MATLAB (R2019b) implementation, the Maple-based approach achieves significantly higher
Xiaojie Dou, Jin-San Cheng, Junyi Wen
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On zeros of polynomial

Ufimskii Matematicheskii Zhurnal, 2019
Summary: For a given polynomial \[P\left( z\right) =z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+\cdots +a_1z+a_0\] with real or complex coefficients, the Cauchy bound \[\left\vert z\right\vert
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Convergence of Comonotone Histopolating Splines

Mathematical Modelling and Analysis, 2015
The convergence rate of histopolation on an interval with combined splines of class C1 having linear/linear rational or quadratic polynomial pieces is studied.
Helle Hallik, Peeter Oja
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On the Zeroes of a Polynomial

Journal of Approximation Theory, 1995
Improving on a result of \textit{J. L. Walsh} [Ann. Math., II. Ser. 25, 285-296 (1924; JFM 50.0045.03)], the author offers the inequality \[ |z+ (a_{n- 1}/2)|\leq |a_{n- 1} |/2+ \Biggl[\sum^n_{j= 2} |a_{n- j}|(\max_{2\leq k\leq n} |a_{n- k}|^{(2- j)/k})^{1/2}\Biggr] \] for zeroes of \(\sum^{n- 1}_{j= 0} a_j z^j+ z^n\) \((n\geq 2)\).
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Speiser’s Theorem on the Road

Walailak Journal of Science and Technology, 2019
In this note we discuss the Gauss-Lucas theorem (for the zeros of the derivative of a polynomial) and Speiser’s equivalent for the Riemann hypothesis (about the location of zeros of the Riemann zeta-function).
Janyarak TONGSOMPORN, Jörn STEUDING
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On the Location of Zeros of Polynomials

American Journal of Computational Mathematics, 2011
In this paper, we prove some extensions and generalizations of the classical Enestrom-Kakeya theorem.
Gulshan Singh, Wali Mohammad Shah
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On the zeros of Meixner polynomials [PDF]

Numerische Mathematik, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alta Jooste, Kerstin Jordaan, Ferenc Toókos   +2 more
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Inequalities for the Polar Derivative of a Polynomial

Abstract and Applied Analysis, 2012
For a polynomial 𝑝(𝑧) of degree 𝑛, we consider an operator 𝐷𝛼 which map a polynomial 𝑝(𝑧) into 𝐷𝛼𝑝(𝑧)∶=(𝛼−𝑧)𝑝′(𝑧)+𝑛𝑝(𝑧) with respect to 𝛼. It was proved by Liman et al. (2010) that if 𝑝(𝑧) has no zeros in |𝑧|
Ahmad Zireh
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