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No Strings Attached
- Author:
-
C. Sidney Burrus
- Subject:
- Mathematics and Statistics, Science and Technology
- Institution Name:
- Connexions
- Collection:
-
Connexions
- Grade Level:
- Post-secondary
- Abstract:
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.
- Course Type:
- Learning Module
- Languages:
- English
- Material Type:
- Readings
- Media Format:
- Graphics/Photos, Text/HTML, Downloadable docs
- Conditions of Use:
-
Creative Commons Attribution 2.0
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Horner's Method for Evaluating and Deflating Polynomials
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