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
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.
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