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An alternating projection algorithm for the “approximate” GCD calculation

Limantseva, O. ORCID: 0000-0003-2764-4415, Halikias, G. ORCID: 0000-0003-1260-1383 and Karcanias, N. (2020). An alternating projection algorithm for the “approximate” GCD calculation. IFAC-PapersOnLine, 53(2), pp. 5837-5842. doi: 10.1016/j.ifacol.2020.12.1630 ISSN 2405-8963


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 least-squares 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 step-lengths. 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 available in CRO: 24 May 2021 09:31
Date deposited: 24 May 2021
Date of acceptance: 26 February 2020
Date of first online publication: 14 April 2021
Text - Published Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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