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 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.

**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