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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
Posted:
July 25, 2002
MathSciNet review:
1937409
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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.
Yu.
A. Al′pin, Bounds for the Perron root of a nonnegative matrix
that take into account the properties of its graph, Mat. Zametki
58 (1995), no. 4, 635–637 (Russian); English
transl., Math. Notes 58 (1995), no. 3-4,
1121–1123 (1996). MR 1378343
(97a:15032), http://dx.doi.org/10.1007/BF02305101
- 2.
Masatoshi
Fujii and Fumio
Kubo, Buzano’s inequality and bounds
for roots of algebraic equations, Proc. Amer.
Math. Soc. 117 (1993), no. 2, 359–361. MR 1088441
(93d:47014), http://dx.doi.org/10.1090/S0002-9939-1993-1088441-X
- 3.
Roger
A. Horn and Charles
R. Johnson, Matrix analysis, Cambridge University Press,
Cambridge, 1990. Corrected reprint of the 1985 original. MR 1084815
(91i:15001)
- 4.
Roger
A. Horn and Charles
R. Johnson, Topics in matrix analysis, Cambridge University
Press, Cambridge, 1991. MR 1091716
(92e:15003)
- 5.
Charles
R. Johnson, A Geršgorin inclusion set for
the field of values of a finite matrix, Proc.
Amer. Math. Soc. 41
(1973), 57–60. MR 0318191
(47 #6738), http://dx.doi.org/10.1090/S0002-9939-1973-0318191-3
- 6.
Morris
Marden, Geometry of polynomials, Second edition. Mathematical
Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966. MR 0225972
(37 #1562)
- 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:
http://dx.doi.org/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
Article copyright:
© Copyright 2002 American Mathematical Society
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