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http://dx.doi.org/10.5666/KMJ.2021.61.4.845

Estimations of Zeros of a Polynomial Using Numerical Radius Inequalities  

Bhunia, Pintu (Department of Mathematics, Jadavpur University)
Bag, Santanu (Department of Mathematics, Vivekananda College For Women)
Nayak, Raj Kumar (Department of Mathematics, Jadavpur University)
Paul, Kallol (Department of Mathematics, Jadavpur University)
Publication Information
Kyungpook Mathematical Journal / v.61, no.4, 2021 , pp. 845-858 More about this Journal
Abstract
We present new bounds for the numerical radius of bounded linear operators and 2 × 2 operator matrices. We apply upper bounds for the numerical radius to the Frobenius companion matrix of a complex monic polynomial to obtain new estimations for the zeros of that polynomial. We also show with numerical examples that our new estimations improve on the existing estimations.
Keywords
Numerical radius; Zeros of polynomials; Frobenius companion matrix;
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1 A. A. Abdurakhmanov, Geometry of a Hausdorff domain in problems of localization of the spectrum of arbitrary matrices, Math. USSR Sb., 59(1988), 39-51.   DOI
2 A. Abu-Omar and F. Kittaneh, Numerical radius inequalities for n×n operator matrices, Linear Algebra Appl., 468(2015), 18-26.   DOI
3 A. Abu-Omar and F. Kittaneh, Upper and lower bounds for the numerical radius with an application to involution operators, Rocky Mountain J. Math., 45(4)(2015), 1055-1065.   DOI
4 A. Abu-Omar and F. Kittaneh, Estimates for the numerical radius and the spectral radius of the Frobenius companion matrix and bounds for the zeros of polynomials, Ann. Funct. Anal., 5(1)(2014), 56-62.   DOI
5 P. Bhunia, S. Bag and K. Paul, Numerical radius inequalities and its applications in estimation of zeros of polynomials, Linear Algebra Appl., 573(2019), 166-177.   DOI
6 P. Bhunia, S. Bag and K. Paul, Bounds for zeros of a polynomial using numerical radius of Hilbert space operators, Ann. Funct. Anal., 12, 21(2021).
7 P. Bhunia, S. Bag and K. Paul, Numerical radius inequalities of operator matrices with applications, Linear Multilinear Algebra, 69(9)(2021), 1635-1644.   DOI
8 S. Bag, P. Bhunia and K. Paul, Bounds of numerical radius of bounded linear operator using t-Aluthge transform, Math. Inequal. Appl., 23(3)(2020), 991-1004.
9 P. Bhunia, K. Paul and R. K. Nayak, Sharp inequalities for the numerical radius of Hilbert space operators and operator matrices, Math. Inequal. Appl., 24(1)(2021), 167-183.
10 M. Fujii and F. Kubo, Buzano's inequality and bounds for roots of algebraic equations, Proc. Amer. Math. Soc., 117(1993), 359-361.   DOI
11 I. B. Jung, E. Ko and C. Pearcy, Aluthge transforms of operators, Integral Equations Operator Theory, 37(2000), 437-448.   DOI
12 K. E. Gustafson and D. K. M. Rao, Numerical Range, The field of values of linear operators and matrices, Springer, New York, 1997.
13 R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
14 O. Hirzallah, F. Kittaneh and K. Shebrawi, Numerical radius inequalities for 2 × 2 operator matrices, Studia Math., 210(2012), 99-115.   DOI
15 F. Kittaneh and K. Shebrawi, Bounds for the zeros of polynomials from matrix inequalities- II, Linear Multilinear Algebra., 55(2007), 147-158.   DOI
16 F. Kittaneh, Bounds for the zeros of polynomials from matrix inequalities, Arch. Math. (Basel), 81(2003), 601-608.   DOI
17 F. Kittaneh, Singular values companion matrices and bounds on zeros of polynomials, Siam J. Matrix Anal. Appl., 16(1995), 333-340.   DOI
18 K. Paul and S. Bag, On the numerical radius of a matrix and estimation of bounds for zeros of a polynomial, Int. J. Math. Math. Sci., 2012(2012) Article Id 129132.
19 K. Shebrawi, Numerical radius inequalities for certain 2×2 operator matrices II, Linear Algebra Appl., 523(2017), 1-12.   DOI
20 T. Yamazaki, On upper and lower bounds of the numerical radius and an equality condition, Studia Math., 178(2007) 83-89.   DOI