Implicit QR with Compression

Paola Boito (1) , Yuli Eidelman , Luca Gemignani , Israel C. Gohberg

1 XLIM-DMI - DMI

In this paper we elaborate on the implicit shifted QR eigenvalue algorithm given in [D. A. Bini, P. Boito, Y. Eidelman, L. Gemignani, I. Gohberg, Linear Algebra Appl. 432 (2010), 2006-2031]. The algorithm is substantially simplified and speeded up while preserving its numerical robustness. This allows us to obtain a potentially important advance towards a proof of its backward stability together with both cost reductions and implementative benefits.

Keywords: Companion matrix; Polynomial roots; Quasiseparable matrices; QR method; Eigenvalue computation

Paola Boito, Yuli Eidelman, Luca Gemignani, Israel C. Gohberg. Implicit QR with Compression. Indagationes Mathematicae, 2012, 23 (4), pp.733-761. ⟨10.1016/j.indag.2012.05.006⟩. ⟨hal-00766711⟩