System theoretic based characterisation and computation of the least common multiple of a set of polynomials.
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.
scientific article; zbMATH DE number 2069717
scientific article