A subspace method for the computation of the GCD of polynomials
type: Item
instance of: scholarly article
title: A subspace method for the computation of the GCD of polynomials
zbMATH Open document ID: 0922.93016
DOI: 10.1016/S0005-1098(96)00244-0
author: Wanzhi Qiu
author: Yingbo Hua
author: Karim Abed-Meraim
published in: Automatica
publication date: 1999-01-19T00:00:00Z
review text: Given a set of polynomials \[ Y_i(s)=y_i(0)+\ldots + y_i(d_i)s^{d_i},\quad i=1,\ldots,M, \] the authors present an algorithm to compute a polynomial \(C(s)\) such that \[ Y_i(s)=C(s) H_i(s),\quad i=1,\ldots,M, \] where \(H_i\), \(i=1,\ldots,M,\) have no common roots. The ideas are based on a concept called subspace method and the algorithm can be simply described by well known linear algebra procedures, with the main computation being the null space of an \(M(d+1) \times 2d+1\) matrix, where \(d=\max\{d_1, \ldots , d_M\}\). Heuristics are presented to indicate that the method is robust if data is prone to noise.
reviewed by: Vilmar Trevisan
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 93B35
zbMATH DE Number: 1038746
zbMATH Keywords: polynomials
zbMATH Keywords: subspace method
zbMATH Keywords: matrix pencil
zbMATH Keywords: GCD
MaRDI profile type: Publication
cites work: Greatest common divisor via generalized Sylvester and Bezout matrices
cites work: A matrix pencil based numerical method for the computation of the GCD of polynomials
cites work: Sensor array processing based on subspace fitting
Wikidata QID: Q127359398
full work available at URL: s0005-1098(96)00244-0
OpenAlex ID: W2074424999
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description: scientific article; zbMATH DE number 1038746