Abstract
Let a monic polynomial P n (x):= x n-a1 x n-1-…-a n ,a j ∈C, j = 1,2,…, n, be given. Bounds for the the numerical radii of some special companion matrices of P n are computed. From these estimates bounds for the zeros of P n are derived.
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References
A. A. Abdurakhmanov, The geometry of the Hausdorff domain in localization problems for the spectrum of arbitrary matrices, Math. USSR Sbornik 59 (1988), 39–51.
M.-T. Chien, On the numerical range of tridiagonal operators, Lin. Alg. Appl. 246 (1996), 203–214.
K. R. Davidson and J. A. R. Holbrook, Numerical radii of zero-one matrices, Michigan Math. J. 35 (1988), 261–267.
M. Fujii and F. Kubo, Buzano’s inequality and bounds for roots of algebraic equations, Proc. Am. Math. Soc. 117 (1993), 359–361.
K. E. Gustafson and D. K. M. Rao, Numerical Range, Springer-Verlag, New York, 1997.
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1990.
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
F. Kittaneh, Singular values of companion matrices and bounds on zeros of polynomials, SIAM J. Matrix Anal. Appl. 16 (1995), 333–340.
H. Linden, Bounds for the zeros of polynomials from eigenvalues and singular values of some companion matrices, Lin. Alg. Appl. 271 (1998), 41–82.
M. Marcus and B. N. Shure, The numerical range of certain 0,1-Matrices, Lin. Alg. Appl. 7 (1979), 111–120.
M. Marden, Geometry of Polynomials, Amer. Math. Soc. Surveys, Vol. 3, 2nd ed., Providence, R. L, 1969.
M. Mignotte, Mathematics for Computer Algebra, Springer, New York, 1992.
G. V. Milovanović, D. S. Mitrinović, and Th. M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapore New Jersey London Hong Kong, 1994.
M. Parodi, La Localisation des Valeurs Caractéristiques des Matrices et ses Applications, Gauthier-Villars, Paris, 1959.
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© 1999 Springer Science+Business Media Dordrecht
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Linden, H. (1999). Numerical Radii of Some Companion Matrices and Bounds for the Zeros of Polynomials. In: Rassias, T.M., Srivastava, H.M. (eds) Analytic and Geometric Inequalities and Applications. Mathematics and Its Applications, vol 478. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4577-0_13
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DOI: https://doi.org/10.1007/978-94-011-4577-0_13
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