System theoretic based characterisation and computation of the least common multiple of a set of polynomials.
type: Item
instance of: scholarly article
title: System theoretic based characterisation and computation of the least common multiple of a set of polynomials.
zbMATH Open document ID: 1049.65011
published in: Linear Algebra and its Applications
publication date: 2004-05-27T00:00:00Z
review text: S new characterization of the least common multiple (LCM) of a set of polynomials \[ {\mathcal P}= \{p_i(s),i\in k: p_i(s)\in \mathbb{R}[s],\,\partial\{p_i(s)\}= d_i\}, \] is presented, where \(\mathbb{R}[s]\) denotes the ring of polynomials over \(\mathbb{R}\) and \(\partial\{\cdot\}\) denotes the degree function. The idea is based on the properties of the controllable space of a linear system and the procedure that is presented leads to an efficient numerical procedure for the computation of LCM and the associated set of multipliers of \({\mathcal P}\) with respect to LCM. The essential part of the numerical procedure is the determination of the successive ranks of parts of the controllability matrix. An general theoretical algorithm is formulated and its numerical properties are investigated. The new method provides a robust procedure for the computation of LCM and enables the computation of approximate values, when the original data are inaccurate.
reviewed by: Costică Moroşanu
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 2069717
zbMATH Keywords: algebraic computations
zbMATH Keywords: least common multiple
zbMATH Keywords: polynomials
zbMATH Keywords: system theory
zbMATH Keywords: algorithm
zbMATH Keywords: controllability matrix
author: Nicos Karcanias
author: Marilena Mitrouli
MaRDI profile type: Publication
full work available at URL: j.laa.2003.11.009
OpenAlex ID: W2120672240
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DOI: 10.1016/J.LAA.2003.11.009
description: scientific article; zbMATH DE number 2069717