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About: Zero location for Polynomials with Random Coefficients

Module by: C. Sidney Burrus. E-mail the author

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Name: Zero location for Polynomials with Random Coefficients
ID: m15578
Language: English (en)
Summary: The zeros of a polynomial with random coefficients cluster around the unit circle in the complex plane. As the degree increases, the roots cluster tighter and tighter to the unit circle. This phenomenon is illustrated here.
Subject: Mathematics and Statistics
Keywords: location, polynomial, root, zero
License: Creative Commons Attribution License CC-BY 3.0
Authors: C. Sidney Burrus (csb@rice.edu)
Copyright Holders: C. Sidney Burrus (csb@rice.edu)
Maintainers: C. Sidney Burrus (csb@rice.edu), Daniel Williamson (dcwill@cnx.org)
Latest version: 1.4 (history)
First publication date: Sep 28, 2007 5:13 am -0500
Last revision to module: Dec 3, 2011 4:35 pm -0600

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Version History

Version: 1.4 Dec 3, 2011 4:35 pm -0600 by C. Sidney Burrus
Changes: 
minor typo corrections
Version: 1.3 May 29, 2009 3:13 pm -0500 by C. Sidney Burrus
Changes: 
clean up
Version: 1.2 May 29, 2009 12:51 pm -0500 by C. Sidney Burrus
Changes: 
clean up
Version: 1.1 Nov 27, 2007 10:03 pm -0600 by C. Sidney Burrus
Changes: 
added links

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The following citation styles comply with the attribution requirements for the license (CC-BY 3.0) of this work:

American Chemical Society (ACS) Style Guide:

Burrus, C. Zero location for Polynomials with Random Coefficients, Connexions Web site. http://cnx.org/content/m15578/1.4/, Dec 3, 2011.

American Medical Assocation (AMA) Manual of Style:

Burrus C. Zero location for Polynomials with Random Coefficients [Connexions Web site]. December 3, 2011. Available at: http://cnx.org/content/m15578/1.4/.

American Psychological Assocation (APA) Publication Manual:

Burrus, C. (2011, December 3). Zero location for Polynomials with Random Coefficients. Retrieved from the Connexions Web site: http://cnx.org/content/m15578/1.4/

Chicago Manual of Style (Bibliography):

Burrus, C.. "Zero location for Polynomials with Random Coefficients." Connexions. December 3, 2011. http://cnx.org/content/m15578/1.4/.

Chicago Manual of Style (Note):

C. Burrus, "Zero location for Polynomials with Random Coefficients," Connexions, December 3, 2011, http://cnx.org/content/m15578/1.4/.

Chicago Manual of Style (Reference, in Author-Date style):

Burrus, C. 2011. Zero location for Polynomials with Random Coefficients. Connexions, December 3, 2011. http://cnx.org/content/m15578/1.4/.

Modern Languages Association (MLA) Style Manual:

Burrus, C.. Zero location for Polynomials with Random Coefficients. Connexions. 3 Dec. 2011 <http://cnx.org/content/m15578/1.4/>.