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The numerical radius and bounds for zeros of a polynomial

Author(s): Yuri A. Alpin; Mao-Ting Chien; Lina Yeh
Journal: Proc. Amer. Math. Soc. 131 (2003), 725-730.
MSC (2000): Primary 15A60, 26C10
Posted: July 25, 2002
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Abstract: Let be a monic polynomial. We obtain two bounds for zeros of via the Perron root and the numerical radius of the companion matrix of the polynomial.

References:

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: 10.1090/S0002-9939-02-06623-6
PII: S 0002-9939(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
Posted: 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
Copyright of article: Copyright 2002, American Mathematical Society


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