期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 213, 期 1, 页码 268-287出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2007.01.006
关键词
unitary matrix; rank structured matrix; eigenvalue computation; pull-through operation
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. (c) 2007 Elsevier B.V. All rights reserved.
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