Halikias, G., Galanis, G., Karcanias, N. and Milonidis, E. (2013). Nearest common root of polynomials, approximate greatest common divisor and the structured singular value. IMA Journal of Mathematical Control and Information, 30(4), pp. 423442. doi: 10.1093/imamci/dns032
Abstract
In this paper the following problem is considered: given two coprime polynomials, find the smallest perturbation in the magnitude of their coefficients such that the perturbed polynomials have a common root. It is shown that the problem is equivalent to the calculation of the structured singular value of a matrix arising in robust control and a numerical solution to the problem is developed. A simple numerical example illustrates the effectiveness of the method for two polynomials of low degree. Finally, problems involving the calculation of the approximate greatest common divisor of univariate polynomials are considered, by proposing a generalization of the definition of the structured singular value involving additional rank constraints.
Publication Type:  Article 

Additional Information:  This is a precopyedited, authorproduced PDF of an article accepted for publication in IMA Journal of Mathematical Control and Information following peer review. The version of record Halikias, G, Galanis, G, Karcanias, N & Milonidis, E (2013). Nearest common root of polynomials, approximate greatest common divisor and the structured singular value. IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 30(4) pp423442 is available online at: http://dx.doi.org/10.1093/imamci/dns032 
Publisher Keywords:  Approximate common root of polynomials, approximate GCD, Sylvester resultant matrix, structured singular value, distance to singularity, structured approximations 
Subjects:  Q Science > QA Mathematics 
Departments:  School of Mathematics, Computer Science & Engineering > Engineering School of Mathematics, Computer Science & Engineering > Engineering > Electrical & Electronic Engineering 
Date Deposited:  10 Jun 2015 10:00 
URI:  https://openaccess.city.ac.uk/id/eprint/7289 

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