A Fast Implicit QR Eigenvalue Algorithm for Companion Matrices

Bini, Dario Andrea and Boito, Paola and Eidelman, Yuli and Gemignani, Luca and Gohberg, Israel (2010) A Fast Implicit QR Eigenvalue Algorithm for Companion Matrices. Linear Algebra and its Applications, 432 (8). pp. 2006-2031. ISSN 0024-3795

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SUMMARY An implicit version of the shifted QR eigenvalue algorithm given in [D.~A.~Bini, Y.~Eidelman, I.~Gohberg, L.~Gemignani, SIAM J. Matrix Anal. Appl. 29 (2007), no. 2, 566--585] is presented for computing the eigenvalues of an $n\times n$ 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.
Item Type: Article Companion matrix, quasiseparable structure, $QR$ iteration, eigenvalue computation, complexity Area01 - Scienze matematiche e informatiche > MAT/08 - Analisi numerica Dipartimenti (until 2012) > DIPARTIMENTO DI MATEMATICA "L. TONELLI" Prof Luca Gemignani 10 Feb 2010 20 Dec 2010 11:48 http://eprints.adm.unipi.it/id/eprint/664