A Fast Implicit QR Eigenvalue Algorithm for Companion Matrices

Dario Andrea Bini , Paola Boito (1) , Y. Eldelman , Luca Gemignani , Israel C. Gohberg

1 DMI

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 x 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.

Domaines: Mathématiques [math]

Dario Andrea Bini, Paola Boito, Y. Eldelman, Luca Gemignani, Israel C. Gohberg. A Fast Implicit QR Eigenvalue Algorithm for Companion Matrices. Linear Algebra and its Applications, 2010, 15th Conference of the International-Linear Algebra-Society Jun 2008 Cancun, 432, pp.2006-2031. ⟨10.1016/j.laa.2009.08.003⟩. ⟨hal-00601708⟩