Locating the eigenvalues of matrix polynomials
Abstract
Some known results for locating the roots of polynomials are extended to the case of matrix polynomials. In particular, a theorem by A.E. Pellet [Bulletin des Sciences Math\'ematiques, (2), vol 5 (1881), pp.393-395], some results of D.A. Bini [Numer. Algorithms 13:179-200, 1996] based on the Newton polygon technique, and recent results of M. Akian, S. Gaubert and M. Sharify (see in particular [LNCIS, 389, Springer p.p.291-303] and [M. Sharify, Ph.D. thesis, \'Ecole Polytechnique, ParisTech, 2011]). These extensions are applied for determining 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.
Cite
@article{arxiv.1206.3632,
title = {Locating the eigenvalues of matrix polynomials},
author = {Dario A. Bini and Vanni Noferini and Meisam Sharify},
journal= {arXiv preprint arXiv:1206.3632},
year = {2012}
}
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