✦ LIBER ✦

Unitary rank structured matrices

✍ Scribed by Steven Delvaux; Marc Van Barel

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 386 KB
Volume: 215
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.03.020

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we describe how one can represent a unitary rank structured matrix in an efficient way as a product of elementary unitary or Givens transformations. We also provide some basic operations for manipulating the representation, such as the transition to zero-creating form, the transition to a unitary/Givens-weight representation, as well as an internal pull-through process of the two branches of the representation. Finally, we characterize how to determine the 'shift' correction term to the rank structure, and we provide some applications to this result.

📜 SIMILAR VOLUMES

Eigenvalue computation for unitary rank

Eigenvalue computation for unitary rank structured matrices

✍ Steven Delvaux; Marc Van Barel 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 286 KB

In this paper we describe how to compute the eigenvalues of a unitary rank structured matrix in two steps. First we perform a reduction of the given matrix into Hessenberg form, next we compute the eigenvalues of this resulting Hessenberg matrix via an implicit QR-algorithm. Along the way, we explai

Neville elimination for rank-structured

Neville elimination for rank-structured matrices

✍ Luca Gemignani 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 166 KB

Transformations to rank structures by un

Transformations to rank structures by unitary similarity

✍ Roberto Bevilacqua; Enrico Bozzo; Gianna M. Del Corso 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 198 KB

We study transformations by unitary similarity of a nonderogatory matrix to certain rank structured matrices. This kind of transformations can be described in a unified framework that involves Krylov matrices. The rank structures here addressed are preserved by QR iterations, and every iterate can b

Eigenvalue perturbation theory of classe

Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations

✍ Christian Mehl; Volker Mehrmann; André C.M. Ran; Leiba Rodman 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 380 KB