Limantseva, O. ORCID: 0000000327644415, Halikias, G. ORCID: 0000000312601383 and Karcanias, N. (2020). An alternating projection algorithm for the “approximate” GCD calculation. IFACPapersOnLine, 53(2), pp. 58375842. doi: 10.1016/j.ifacol.2020.12.1630 ISSN 24058963
Abstract
In the paper an approach is proposed for calculating the “best” approximate GCD of a set of coprime polynomials. The algorithm is motivated by the factorisation of the Sylvester resultant matrix of polynomial sets with nontrivial GCD. In the (generic) case of coprime polynomial sets considered here the aim is to minimise the norm of the residual error matrix of the inexact factorisation in order to compute the “optimal” approximate GCD. A leastsquares alternating projection algorithm is proposed as an alternative to the solution of the corresponding optimisation problem via nonlinear programming techniques. The special structure of the problem in this case, however, means that the algorithm can be reduced to a sequence of standard subspace projections and hence no need arises to compute gradient vectors, Hessian matrices or optimal steplengths. An estimate of the asymptotic convergence rate of the algorithm is finally established via the inclination of two subspaces.
Publication Type:  Conference or Workshop Item (Paper) 

Publisher Keywords:  nonlinear least squares, Sylvester resultant matrix, approximate GCD, alternating projection algorithm, convergence analysis 
Subjects:  Q Science > QA Mathematics 
Departments:  School of Mathematics, Computer Science & Engineering > Engineering > Electrical & Electronic Engineering 
Date Deposited:  24 May 2021 09:31 
URI:  https://openaccess.city.ac.uk/id/eprint/26164 

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