scholarly journals On Numerical Radius of a Matrix and Estimation of Bounds for Zeros of a Polynomial

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Kallol Paul ◽  
Santanu Bag
Keyword(s):  
Spectral Radius ◽  
Upper Bounds ◽  
Numerical Radius ◽  
Bounds For Zeros

We obtain inequalities involving numerical radius of a matrixA∈Mn(ℂ). Using this result, we find upper bounds for zeros of a given polynomial. We also give a method to estimate the spectral radius of a given matrixA∈Mn(ℂ)up to the desired degree of accuracy.

scholarly journals General numerical radius inequalities for matrices of operators

2016 ◽  
Vol 14 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Mohammed Al-Dolat ◽  
Khaldoun Al-Zoubi ◽  
Mohammed Ali ◽  
Feras Bani-Ahmad
Keyword(s):  
Lower Bounds ◽  
Upper Bounds ◽  
Zeros Of Polynomials ◽  
Numerical Radius

AbstractLet Ai ∈ B(H), (i = 1, 2, ..., n), and $ T = \left[ {\matrix{ 0 & \cdots & 0 & {A_1 } \cr \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {A_2 } & 0 \cr 0 & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots \cr {A_n } & 0 & \cdots & 0 \cr } } \right] $ . In this paper, we present some upper bounds and lower bounds for w(T). At the end of this paper we drive a new bound for the zeros of polynomials.

A novel numerical radius upper bounds for 2 × 2 operator matrices

2020 ◽  
pp. 1-12
Author(s):  
Mohammed Al-Dolat ◽  
Imad Jaradat ◽  
Baráa Al-Husban
Keyword(s):  
Upper Bounds ◽  
Operator Matrices ◽  
Numerical Radius

scholarly journals The numerical radius and bounds for zeros of a polynomial

2002 ◽  
Vol 131 (3) ◽  
pp. 725-730 ◽  
Author(s):  
Yuri A. Alpin ◽  
Mao-Ting Chien ◽  
Lina Yeh
Keyword(s):  
Numerical Radius ◽  
Bounds For Zeros

scholarly journals Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yajing Wang ◽  
Yubin Gao
Keyword(s):  
Graph Theory ◽  
Spectral Radius ◽  
Adjacency Matrix ◽  
Upper Bounds ◽  
Simple Graph ◽  
Spectral Graph Theory ◽  
Extremal Graphs ◽  
Spectral Graph ◽  
Vertex Set

Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new upper bounds on arithmetic-geometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.

scholarly journals Sharp Upper Bounds for the Laplacian Spectral Radius of Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Houqing Zhou ◽  
Youzhuan Xu
Keyword(s):  
Spectral Radius ◽  
Transient Stability ◽  
Laplacian Matrix ◽  
Schwarz Inequality ◽  
Upper Bounds ◽  
Power Network ◽  
Laplacian Eigenvalue ◽  
Laplacian Spectral Radius ◽  
Wide Range ◽  
Simple Connected Graph

The spectrum of the Laplacian matrix of a network plays a key role in a wide range of dynamical problems associated with the network, from transient stability analysis of power network to distributed control of formations. LetG=(V,E)be a simple connected graph onnvertices and letμ(G)be the largest Laplacian eigenvalue (i.e., the spectral radius) ofG. In this paper, by using the Cauchy-Schwarz inequality, we show that the upper bounds for the Laplacian spectral radius ofG.

scholarly journals The Spectral Radius for a Class of Double-Star-Like Tree Systems with Maximal Degree 4

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Yufeng Mao ◽  
Meijin Xu ◽  
Xiaodong Chen ◽  
Yan-Jun Liu ◽  
Kai Li
Keyword(s):  
Spectral Radius ◽  
Transformation Method ◽  
Upper Bounds ◽  
Double Star ◽  
Maximal Degree ◽  
Extremal Graphs ◽  
Second Degree

We mainly study the properties of the 4-double-star-like tree, which is the generalization of star-like trees. Firstly we use graft transformation method to obtain the maximal and minimum extremal graphs of 4-double-star-like trees. Secondly, by the relations between the degree and second degree of vertices in maximal extremal graphs of 4-double-star-like trees we get the upper bounds of spectral radius of 4-double-star-like trees.

Sign in / Sign up

Export Citation Format

Share Document