Nearest common root of polynomials, approximate greatest common divisor and the structured singular value

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), pp. 423-442. doi: 10.1093/imamci/dns032

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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.

Item Type: Article
Additional Information: This is a pre-copyedited, author-produced 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) pp423-442 is available online at: http://dx.doi.org/10.1093/imamci/dns032
Uncontrolled Keywords: Approximate common root of polynomials, approximate GCD, Sylvester resultant matrix, structured singular value, distance to singularity, structured approximations
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Engineering
URI: http://openaccess.city.ac.uk/id/eprint/7289

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