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Estimations of Zeros of a Polynomial Using Numerical Radius Inequalities

Pintu Bhunia|Santanu Bag|Raj Kumar Nayak|Kallol Paul
경북대학교 자연과학대학 수학과|2021.12|Kyungpook Mathematical Journal|제61권 제4호|pp. 845-858

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키워드

Numerical radiusZeros of polynomialsFrobenius companion matrix
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초록

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.

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.

참고문헌 (20)

  1. A. A. Abdurakhmanov, "Geometry of a Hausdorff domain in problems of localization of the spectrum of arbitrary matrices", Math. USSR Sb, 59, pp.39~51 (1988)
  2. A. Abu-Omar, "Numerical radius inequalities for n×n operator matrices", Linear Algebra Appl, 468, pp.18~26 (2015)
  3. A. Abu-Omar, "Upper and lower bounds for the numerical radius with an application to involution operators", Rocky Mountain J. Math, 45(4), pp.1055~1065 (2015)
  4. A. Abu-Omar, "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), pp.56~62 (2014)
  5. P. Bhunia, "Numerical radius inequalities and its applications in estimation of zeros of polynomials", Linear Algebra Appl, 573, pp.166~177 (2019)
  6. P. Bhunia, "Numerical radius inequalities of operator matrices with applications", Linear Multilinear Algebra, 69(9), pp.1635~1644 (2021)
  7. S. Bag, "Bounds of numerical radius of bounded linear operator using t-Aluthge transform", Math. Inequal. Appl, 23(3), pp.991~1004 (2020)
  8. P. Bhunia, "Bounds for zeros of a polynomial using numerical radius of Hilbert space operators", Ann. Funct. Anal, 12, pp.21~ (2021)
  9. P. Bhunia, "Sharp inequalities for the numerical radius of Hilbert space operators and operator matrices", Math. Inequal. Appl, 24(1), pp.167~183 (2021)
  10. M. Fujii, "Buzano’s inequality and bounds for roots of algebraic equations", Proc. Amer. Math. Soc, 117, pp.359~361 (1993)
  11. K. E. Gustafson, "Numerical Range, The field of values of linear operators and matrices" (1997), Springer
  12. R. A. Horn, "Matrix Analysis" (1985), Cambridge University Press
  13. O. Hirzallah, "Numerical radius inequalities for 2 × 2 operator matrices", Studia Math, 210, pp.99~115 (2012)
  14. I. B. Jung, "Aluthge transforms of operators", Integral Equations Operator Theory, 37, pp.437~448 (2000)
  15. F. Kittaneh, "Bounds for the zeros of polynomials from matrix inequalities-II", Linear Multilinear Algebra, 55, pp.147~158 (2007)
  16. F. Kittaneh, "Bounds for the zeros of polynomials from matrix inequalities", Arch. Math. (Basel), 81, pp.601~608 (2003)
  17. F. Kittaneh, "Singular values companion matrices and bounds on zeros of polynomials", Siam J. Matrix Anal. Appl, 16, pp.333~340 (1995)
  18. K. Paul, "On the numerical radius of a matrix and estimation of bounds for zeros of a polynomial", Int. J. Math. Math. Sci, 2012 (2012)
  19. K. Shebrawi, "Numerical radius inequalities for certain 2×2 operator matrices II", Linear Algebra Appl, 523, pp.1~12 (2017)
  20. T. Yamazaki, "On upper and lower bounds of the numerical radius and an equality condition", Studia Math, 178, pp.83~89 (2007)

관련 논문AI추천

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