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

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Name: Horner's Method for Evaluating and Deflating Polynomials
ID: m15099
Language: English (en)
Summary: Horner's method is a standard minimum arithmetic method for evaluating and deflating polynomials. It can also efficiently evaluate various order derivatives of a polynomial, therefore is often used as part of Newton's method. This note tries to develop the various techniques called Horner's method, nested evaluation, and synthetic division in a common framework using a recursive structure and difference equations. There is a similarity to Goertzel's algorithm for the DFT, Z-transform inversion by division, and Pade's and Prony's methods. This approach also allows a straight forward explanation of "stability" or numerical errors of the algorithms. Matlab implementations are given. This note came from the work of the "Polynomial Club" at Rice: Burrus, Fox, Sitton, and Treitel.
Subject: Mathematics and Statistics
Keywords: deflate polynomial, evaluate polynomial, Horner's method, nested evaluation, Newton's method, polynomial, synthetic division
Document Type: -//CNX//DTD CNXML 0.5 plus MathML//EN
License: Creative Commons Attribution License CC-BY 2.0
Authors: C. Sidney Burrus (csb@rice.edu)
Copyright Holders: C. Sidney Burrus (csb@rice.edu)
Maintainers: C. Sidney Burrus (csb@rice.edu)
Latest version: 1.6 (history)
First publication date: Sep 14, 2007 8:43 am GMT-5
Last revision to module: Nov 28, 2007 12:20 pm US/Central

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Version History

Version: 1.6 Nov 28, 2007 12:20 pm US/Central by C. Sidney Burrus
Changes: 
 link
Version: 1.5 Nov 28, 2007 9:23 am US/Central by C. Sidney Burrus
Changes: 
 added links
Version: 1.4 Nov 28, 2007 9:17 am US/Central by C. Sidney Burrus
Changes: 
 fix typos
Version: 1.3 Nov 27, 2007 9:04 am US/Central by C. Sidney Burrus
Changes: 
minor clean up.
Version: 1.2 Sep 22, 2007 4:56 pm GMT-5 by C. Sidney Burrus
Changes: 
added flow graph figure, one .png for screen use and one .eps for printing
Version: 1.1 Sep 14, 2007 1:02 pm GMT-5 by C. Sidney Burrus
Changes: 
general clean up

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Burrus, C. Horner's Method for Evaluating and Deflating Polynomials, Connexions Web site. http://cnx.org/content/m15099/1.6/, Nov 28, 2007.

American Medical Assocation (AMA) Manual of Style:

Burrus C. Horner's Method for Evaluating and Deflating Polynomials [Connexions Web site]. November 28, 2007. Available at: http://cnx.org/content/m15099/1.6/.

American Psychological Assocation (APA) Publication Manual:

Burrus, C. (2007, November 28). Horner's Method for Evaluating and Deflating Polynomials. Retrieved from the Connexions Web site: http://cnx.org/content/m15099/1.6/

Chicago Manual of Style (Bibliography):

Burrus, C.. "Horner's Method for Evaluating and Deflating Polynomials." Connexions. November 28, 2007. http://cnx.org/content/m15099/1.6/.

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C. Burrus, "Horner's Method for Evaluating and Deflating Polynomials," Connexions, November 28, 2007, http://cnx.org/content/m15099/1.6/.

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

Burrus, C. 2007. Horner's Method for Evaluating and Deflating Polynomials. Connexions, November 28, 2007. http://cnx.org/content/m15099/1.6/.

Modern Languages Association (MLA) Style Manual:

Burrus, C.. Horner's Method for Evaluating and Deflating Polynomials. Connexions. 28 Nov. 2007 <http://cnx.org/content/m15099/1.6/>.