A Fast Implicit QR Eigenvalue Algorithm for Companion Matrices

  title={A Fast Implicit QR Eigenvalue Algorithm for Companion Matrices},
  author={Dario Bini and Paola Boito and Yuli Eidelman and Luca Gemignani and Israel Gohberg},
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 × n companion matrix using O(n2) flops and O(n) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method. 
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