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Eigenvalue computation for unitary rank structured matrices

✍ Scribed by Steven Delvaux; Marc Van Barel

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
286 KB
Volume
213
Category
Article
ISSN
0377-0427

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✦ Synopsis

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 explain how the knowledge of a certain 'shift' correction term to the structure can be used to speed up the QR-algorithm for unitary Hessenberg matrices, and how this observation was implicitly used in a paper due to William B. Gragg. We also treat an analogue of this observation in the Hermitian tridiagonal case.

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Unitary rank structured matrices
Unitary rank structured matrices
✍ Steven Delvaux; Marc Van Barel πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 386 KB

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 t