Results 21 to 30 of about 2,960 (152)

A note on the structure of the zeros of a polynomial and Sendov's conjecture

Cubo, 2023
In this note we prove a result that highlights an interesting connection between the structure of the zeros of a polynomial \(p(z)\) and Sendov's conjecture.
G. M. Sofi, W. M. Shah
doaj   +1 more source

Annular Bounds for the Zeros of a Polynomial

International Journal of Mathematics and Mathematical Sciences, 2018
The problem of obtaining the smallest possible region containing all the zeros of a polynomial has been attracting more and more attention recently, and in this paper, we obtain several results providing the annular regions that contain all the zeros of ...
Le Gao, N. K. Govil
doaj   +1 more source

Zeros of unilateral quaternionic polynomials [PDF]

The Electronic Journal of Linear Algebra, 2006
The purpose of this paper is to show how the problem of finding the zeros of unilateral n-order quaternionic polynomials can be solved by determining the eigen-vectors of the corresponding companion matrix. This approach, probably superfluous in the case of quadratic equations for which a closed formula can be given, becomes truly useful for ...
De Leo, Stefano, Ducati, Gisele, Leonardi, Vinicius   +2 more
openaire   +2 more sources

Bounds for the zeros of unilateral octonionic polynomials

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix.
Serôdio Rogério, Beites P. D., Vitória José   +2 more
doaj   +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
doaj   +1 more source

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
openaire   +1 more source

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
doaj   +1 more source

Nowhere-zero flow polynomials

Journal of Combinatorial Theory, Series A, 2004
In this article we introduce the flow polynomial of a digraph and use it to study nowhere-zero flows from a commutative algebraic perspective. Using Hilbert's Nullstellensatz, we establish a relation between nowhere-zero flows and dual flows. For planar graphs this gives a relation between nowhere-zero flows and flows of their planar duals.
openaire   +3 more sources

$q$-Eulerian Polynomials and Polynomials with Only Real Zeros [PDF]

The Electronic Journal of Combinatorics, 2008
Let $f$ and $F$ be two polynomials satisfying $F(x)=u(x)f(x)+v(x)f'(x)$. We characterize the relation between the location and multiplicity of the real zeros of $f$ and $F$, which generalizes and unifies many known results, including the results of Brenti and Brändén about the $q$-Eulerian polynomials.
Ma, Shi-Mei, Wang, Yi
openaire   +3 more sources

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
doaj   +1 more source