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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The generalisation of the method to calculate the approximate greatest common divisor of polynomials is discussed and it is shown that the problem is equivalent to the calculation of the structured singular value of a matrix, which can be performed using efficient existing techniques of robust control.
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