Locating the eigenvalues of matrix polynomials

2012/06/16 by Dario A. Bini, Vanni Noferini, Bini, Dario A. +3 · 2 citations
Computer Science · Mathematics · #Matrix Theory and Algorithms #Iterative Methods for Nonlinear Equations #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.1206.3632

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 Mathématiques, (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, École 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.

Cited by

• Generalizations of Enestrom-Kakeya Type Theorems for matrix Polynomials
• Generalization of Cauchy type theorems for matrix Polynomials

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