On efficient computation and asymptotic sharpness of Kalantari's bounds for zeros of polynomials
Author:
Yi Jin
Journal:
Math. Comp. 75 (2006), 1905-1912
MSC (2000):
Primary 12D10, 65H05, 68Q25; Secondary 05A15, 11B37
DOI:
https://doi.org/10.1090/S0025-5718-06-01868-0
Published electronically:
June 28, 2006
MathSciNet review:
2240641
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We study an infinite family of lower and upper bounds on the modulus of zeros of complex polynomials derived by Kalantari. We first give a simple characterization of these bounds which leads to an efficient algorithm for their computation. For a polynomial of degree our algorithm computes the first
bounds in Kalantari's family in
operations. We further prove that for every complex polynomial these lower and upper bounds converge to the tightest annulus containing the roots, and thus settle a problem raised in Kalantari's paper.
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Additional Information
Yi Jin
Affiliation:
Department of Computer Science, Rutgers University, New Brunswick, New Jersey 08901
Email:
yjin@paul.rutgers.edu
DOI:
https://doi.org/10.1090/S0025-5718-06-01868-0
Keywords:
Bounds on polynomial roots,
asymptotic sharpness,
generating functions,
recurrence relations
Received by editor(s):
January 14, 2005
Received by editor(s) in revised form:
August 3, 2005
Published electronically:
June 28, 2006
Article copyright:
© Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.