Polynomial GCD derived through monic polynomial subtractions
type: Item
instance of: scholarly article
title: Polynomial GCD derived through monic polynomial subtractions
zbMATH Open document ID: 1245.12007
DOI: 10.5402/2011/714102
author: Feng Cheng Chang
published in: ISRN Applied Mathematics
publication date: 2012-05-21T00:00:00Z
review text: The computation of the greatest common divisor (GCD) of a pair of polynomials is an important issue in computational mathematics and also plays a crucial role in many science and engineering fields. Several numerical methods have been proposed for the derivation of polynomial GCD. Some are based on the classical Euclidean algorithm and the others are based on the procedures involving Sylvester resultant matrix. Most of them require an algorithm of some advanced mathematics, such as the singular value decomposition and the least square iteration process. In this paper a simple and effective method to find the GCD of a pair of given polynomials is presented. The process requires only the successive subtraction of two monic polynomials. It is modified purposely from the longhand polynomial divisions employed in the classical Euclidean GCD computation. The entire computations require only simple elementary arithmetic operations, such as division and subtraction. A MATLAB code is provided, along with a typical numerical example. Amazingly, this routine gives the GCD for a pair of test polynomials of very high degree.
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 6037045
Wikidata QID: Q58689531
describes a project that uses: MultRoot
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2011/714102
OpenAlex ID: W2027693029
cites work: Computing multiple roots of inexact polynomials
cites work: Method for finding multiple roots of polynomials
cites work: Recursive polynomial remainder sequence and its subresultants
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description: scientific article; zbMATH DE number 6037045