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The numerical radius and bounds for zeros of a polynomial


Authors: Yuri A. Alpin, Mao-Ting Chien and Lina Yeh
Journal: Proc. Amer. Math. Soc. 131 (2003), 725-730
MSC (2000): Primary 15A60, 26C10
DOI: https://doi.org/10.1090/S0002-9939-02-06623-6
Published electronically: July 25, 2002
MathSciNet review: 1937409
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $p(t)$ be a monic polynomial. We obtain two bounds for zeros of $p(t)$ via the Perron root and the numerical radius of the companion matrix of the polynomial.


References [Enhancements On Off] (What's this?)

  • 1. Y. A. Alpin, Bounds for the Perron root of a nonnnegative matrix involving the properties of its graph, Math. Notes 58(1995), 1121-1123. MR 97a:15032
  • 2. M. Fujii and F. Kubo, Buzano's inequality and bounds for roots of algebraic equations, Proc. Amer. Math. Soc. 117(1993), 359-361. MR 93d:47014
  • 3. R. A. Horn and C. R. Johnson, Matrix analysis, Camb. Univ. Press, New York, 1990. MR 91i:15001
  • 4. R. A. Horn and C. R. Johnson, Topics in matrix analysis, Camb. Univ. Press, New York, 1991. MR 92e:15003
  • 5. C. R. Johnson, A Gersgorin inclusion set for the field of values of a finite matrix, Proc. Amer. Math. Soc. 41(1973), 57-60. MR 47:6738
  • 6. M. Marden, Geometry of polynomials, Math. Surveys and Monographs, No. 3, Amer. Math. Soc., 1989. MR 37:1562 (review of 2nd edition)

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Additional Information

Yuri A. Alpin
Affiliation: Department of Mathematics and Mechanics, Kazan State University, Kazan, Russia, 420008
Email: Yuri.Alpin@ksu.ras.ru

Mao-Ting Chien
Affiliation: Department of Mathematics, Soochow University, Taipei, Taiwan 11102
Email: mtchien@math.scu.edu.tw

Lina Yeh
Affiliation: Department of Mathematics, Soochow University, Taipei, Taiwan 11102
Email: yehlina@math.scu.edu.tw

DOI: https://doi.org/10.1090/S0002-9939-02-06623-6
Keywords: Perron root, numerical range, numerical radius, companion matrix
Received by editor(s): December 14, 1999
Received by editor(s) in revised form: October 24, 2001
Published electronically: July 25, 2002
Additional Notes: The work of the second author was supported by the National Science Council of the Republic of China.
Communicated by: David Sharp
Article copyright: © Copyright 2002 American Mathematical Society

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