scholarly journals Bounds for the zeros of polynomials from compression matrix inequalities

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 1035-1051
Author(s):  
Fuad Kittaneh ◽  
Mohammad Odeh ◽  
Khalid Shebrawi
Keyword(s):  
Upper Bounds ◽  
Zeros Of Polynomials ◽  
Matrix Inequalities ◽  
Companion Matrices

In this paper, some compression matrix inequalities are applied to the Frobenius companion matrices of monic polynomials in order to obtain new upper bounds for the zeros of such polynomials.

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.

Delayed-Decomposition Approach for Absolute Stability of Neutral-Type Lurie Control Systems With Time-Varying Delays

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Control Systems ◽  
Lyapunov Functional ◽  
Absolute Stability ◽  
Neutral Type ◽  
Upper Bounds ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Decomposition Approach ◽  
Delay Dependent

The problem of absolute stability for a class of neutral-type Lurie control system with nonlinearity located in an infinite sector and in a finite one is investigated in this paper. Based on the delayed-decomposition approach (DDA), a new augmented Lyapunov functional is constructed and the delay dependent conditions for asymptotic stability are derived by applying an integral inequality approach (IIA) in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.

scholarly journals Upper bounds for the separation of real zeros of polynomials

1996 ◽  
Vol 39 (2) ◽  
pp. 357-363 ◽  
Author(s):  
Peter Walker
Keyword(s):  
Inverse Operator ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Zeros Of Polynomials ◽  
Real Zeros

Let be a polynomial with distinct real zeros whose separation is defined by δ(f) = min i≠j(ai-aj ). We establish upper estimates for δ(f′-kf) in terms of n, k, and δ(f). The results give sufficient conditions for the inverse operator (D – kl)−1 to preserve the reality of the zeros of a polynomial.

scholarly journals Some Upper Matrix Bounds for the Solution of the Continuous Algebraic Riccati Matrix Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zübeyde Ulukök ◽  
Ramazan Türkmen
Keyword(s):  
Matrix Equation ◽  
Equivalent Form ◽  
Upper Bounds ◽  
Matrix Inequalities ◽  
Numerical Example ◽  
Riccati Matrix Equation ◽  
Solution Matrix ◽  
Riccati Matrix

We propose diverse upper bounds for the solution matrix of the continuous algebraic Riccati matrix equation (CARE) by building the equivalent form of the CARE and using some matrix inequalities and linear algebraic techniques. Finally, numerical example is given to demonstrate the effectiveness of the obtained results in this work as compared with some existing results in the literature. These new bounds are less restrictive and provide more efficient results in some cases.

Bounds for the zeros of polynomials from matrix inequalities – II

2007 ◽  
Vol 55 (2) ◽  
pp. 147-158 ◽  
Author(s):  
Fuad Kittaneh ◽  
Khalid Shebrawi
Keyword(s):  
Zeros Of Polynomials ◽  
Matrix Inequalities
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