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(n2) flops and O(n) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method.