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Locating the Eigenvalues of Matrix Polynomials

Bini, DA and Noferini, V and Sharify, M (2013) 'Locating the Eigenvalues of Matrix Polynomials.' SIAM Journal on Matrix Analysis and Applications, 34 (4). 1708 - 1727. ISSN 0895-4798

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Abstract

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, Scaling Algorithms and Tropical Methods in Numerical Matrix Analysis: Application to the Optimal Assignment Problem and to the Accurate Computation of Eigenvalues, Ph.D. thesis, École Polytechnique, Paris, 2011]). These extensions are applied to determine effective initial approximations for the numerical computation of the eigenvalues of matrix polynomials by means of simultaneous iterations, like the Ehrlich--Aberth method. Numerical experiments that show the computational advantage of these results are presented.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 03 Jan 2018 14:10
Last Modified: 03 Jan 2018 15:15
URI: http://repository.essex.ac.uk/id/eprint/20868

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