A fast implicit QR eigenvalue algorithm for companion matrices

An implicit version of the shifted QR eigenvalue algorithm given in Bini et al. [D.A. Bini, Y. Eidelman, I. Gohberg, L. Gemignani, SIAM J. Matrix Anal. Appl. 29(2) (2007) 566–585] is presented for computing the eigenvalues of an n × n companion matrix using O ( n 2 ) flops and O ( n ) memory storage...

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Veröffentlicht in:	Linear algebra and its applications 2010-04, Vol.432 (8), p.2006-2031
Hauptverfasser:	Bini, D.A., Boito, P., Eidelman, Y., Gemignani, L., Gohberg, I.
Format:	Artikel
Sprache:	eng
Schlagworte:	[formula omitted] iteration Algebra Companion matrix Complexity Eigenvalue computation Exact sciences and technology Linear and multilinear algebra, matrix theory Mathematics Quasiseparable structure Sciences and techniques of general use
Online-Zugang:	Volltext
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Zusammenfassung:	An implicit version of the shifted QR eigenvalue algorithm given in Bini et al. [D.A. Bini, Y. Eidelman, I. Gohberg, L. Gemignani, SIAM J. Matrix Anal. Appl. 29(2) (2007) 566–585] is presented for computing the eigenvalues of an n × n companion matrix using O ( n 2 ) flops and O ( n ) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method.
ISSN:	0024-3795 1873-1856
DOI:	10.1016/j.laa.2009.08.003