A fast implicit QR eigenvalue algorithm for companion matrices

作者：Bini D A; Boito P; Eidelman Y; Gemignani L^*; Gohberg I

来源：Linear Algebra and Its Applications, 2010, 432(8): 2006-2031.

DOI：10.1016/j.laa.2009.08.003

• Companion matrix
• Quasiseparable structure
• QR iteration
• Eigenvalue computation
• Complexity

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.

• 出版日期2010-4-1