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

@article{Halikias2013NearestCR,
  title={Nearest common root of polynomials, approximate greatest common divisor and the structured singular value},
  author={George D. Halikias and G. Galanis and Nicos Karcanias and Efstathios Milonidis},
  journal={IMA J. Math. Control. Inf.},
  year={2013},
  volume={30},
  pages={423-442}
}
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… 
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Nearest common root of a set of polynomials: A structured singular value approach
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