Factorization of polynomials based on the multiplicities of their roots and applications
type: Item
instance of: scholarly article
title: Factorization of polynomials based on the multiplicities of their roots and applications
zbMATH Open document ID: 0865.65027
DOI: 10.1016/0898-1221(96)00174-5
author: O. Diekmann
publication date: 1997-07-20T00:00:00Z
review text: A method which enables the polynomial \(d(\lambda)\) of the distinct roots of a polynomial \(p(\lambda)\) to be computed by simple algebraic manipulations of the coefficients of \(p(\lambda)\) is examined. In other words, \(d(\lambda)\) is computed by performing only additions and multiplications of the coefficients of \(p(\lambda)\), and not by computing any roots of \(p(\lambda)\). This method of extracting polynomials of distinct roots is then utilized to develop an algorithm for factoring a polynomial in such a way that one can determine the distinct multiplicities of the roots and the number of distinct roots that have a given multiplicity. Finally, both the extraction method and the factorization process are utilized to develop an algorithm for computing the greatest common divisor of a system of polynomials. In a submitted paper of the authors a code is presented which implements the developed algorithm for factorization based on multiplicity.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 12Y05
zbMATH DE Number: 978115
zbMATH Keywords: Newton's identities
zbMATH Keywords: discriminants
zbMATH Keywords: polynomial of distinct roots
zbMATH Keywords: factorization based on multiplicity
zbMATH Keywords: algorithm
zbMATH Keywords: extraction method
zbMATH Keywords: greatest common divisor
zbMATH Keywords: system of polynomials
reviewed by: Violeta A. Kostova
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00174-5
OpenAlex ID: W2037898649
cites work: Introduction to vectors and tensors. Vol. 1: Linear and multilinear algebra. Vol. 2: Vector and tensor analysis
cites work: Q5614003
cites work: Q3903085
cites work: Q5807694
cites work: Q3105730
cites work: A direct algorithm for extracting a transfer function's multiple zeros or poles
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 978115