Abstract
The paper provides a system theoretic characterisation of the least common multiple (LCM) m( s) of a given set of polynomials P which leads to an efficient numerical procedure for the computation of LCM that avoids root finding and use of greatest common divisor (GCD) procedures. The procedure that is presented also leads to the computation of the associated set of multipliers of P with respect to LCM. The basis of the new characterisation and computational procedure are the controllability properties of a natural realization S(A, b,C) associated with the set P . It is shown, that the coefficients of the LCM are defined by the properties of the controllable subspace of the pair (A, b) , which also leads to the characterisation of associated multipliers. An algorithmic procedure that exploits the companion structure of A 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 innacurate.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.