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2015 Geometric aspects of Pellet's and related theorems
A. Melman
Rocky Mountain J. Math. 45(2): 603-623 (2015). DOI: 10.1216/RMJ-2015-45-2-603

Abstract

Pellet's theorem determines when the zeros of a polynomial can be separated into two regions, according to their moduli. We refine one of those regions and replace it with the closed interior of a lemniscate that provides more precise information on the location of the zeros. Moreover, Pellet's theorem is considered the generalization of a zero inclusion region due to Cauchy. Using linear algebra tools, we derive a different generalization that leads to a sequence of smaller inclusion regions, which are also the closed interiors of lemniscates.

Citation

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A. Melman. "Geometric aspects of Pellet's and related theorems." Rocky Mountain J. Math. 45 (2) 603 - 623, 2015. https://doi.org/10.1216/RMJ-2015-45-2-603

Information

Published: 2015
First available in Project Euclid: 13 June 2015

zbMATH: 1328.12002
MathSciNet: MR3356630
Digital Object Identifier: 10.1216/RMJ-2015-45-2-603

Subjects:
Primary: 12D10, 15A18‎, 30C15

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 2 • 2015
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