Locating the Eigenvalues of Matrix Polynomials

@article{Bini2013LocatingTE,
  title={Locating the Eigenvalues of Matrix Polynomials},
  author={Dario Bini and V. Noferini and M. Sharify},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2013},
  volume={34},
  pages={1708-1727}
}
Some known results for locating the roots of polynomials are extended to the case of matrix polynomials. In particular, a theorem by Pellet [Bull. Sci. Math. (2), 5 (1881), pp. 393--395], some results from Bini [Numer. Algorithms, 13 (1996), pp. 179--200] based on the Newton polygon technique, and recent results from Gaubert and Sharify (see, in particular, [Tropical scaling of polynomial matrices, Lecture Notes in Control and Inform. Sci. 389, Springer, Berlin, 2009, pp. 291--303] and [Sharify… Expand
Tropical Roots as Approximations to Eigenvalues of Matrix Polynomials
Cauchy, Gershgorin, and Matrix Polynomials
Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots
On Descartes' rule of signs for matrix polynomials
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