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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The location of the zeros of the higher order derivatives of a polynomial


Author: Piotr Pawlowski
Journal: Proc. Amer. Math. Soc. 127 (1999), 1493-1497
MSC (1991): Primary 30C15; Secondary 65E05
Published electronically: February 4, 1999
MathSciNet review: 1476386
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Abstract: Let $\displaystyle{p(z)}$ be a complex polynomial of degree $\displaystyle{n}$ having $\displaystyle{k}$ zeros in a disk $\displaystyle{D}$. We deal with the problem of finding the smallest concentric disk containing $\displaystyle{k-l}$ zeros of $\displaystyle{p^{(l)}(z)}$. We obtain some estimates on the radius of this disk in general as well as in the special case, where $\displaystyle{k}$ zeros in $\displaystyle{D}$ are isolated from the other zeros of $\displaystyle{p(z)}$. We indicate an application to the root-finding algorithms.


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Additional Information

Piotr Pawlowski
Affiliation: Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242
Address at time of publication: Summit Systems, Inc., 22 Cortlandt Street, New York, New York 10007
Email: ppawlows@mcs.kent.edu, piotr_pawlowski@summithq.com

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04695-X
PII: S 0002-9939(99)04695-X
Received by editor(s): February 5, 1997
Received by editor(s) in revised form: September 3, 1997
Published electronically: February 4, 1999
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society