The restarted QR-algorithm for eigenvalue computation of structured matrices
نویسندگان
چکیده
منابع مشابه
Eigenvalue computation for unitary rank structured matrices
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 explainhow the knowledge of a certain ‘shift’ correction term to the structure can be used to speed up ...
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Article history: Received 5 November 2008 Accepted 3 August 2009 Available online 4 September 2009 Submitted by V. Olshevsky AMS classification: 65F15 65H17
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In this paper we show how to perform in an explicit way the shifted QR-algorithm for computing the eigenvalues of a rank structured matrix. The implementation is based on the underlying preservation of rank structure under the QR-algorithm. It will be expressed in terms of the Givens-weight/unitary-weight representation which we introduced in a previous paper. The results of some numerical expe...
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It has been shown in [4, 5, 6, 31] that the Hessenberg iterates of a companion matrix under the QR iterations have low off-diagonal rank structures. Such invariant rank structures were exploited therein to design fast QR iteration algorithms for finding eigenvalues of companion matrices. These algorithms require only O(n) storage and run in O(n) time where n is the dimension of the matrix. In t...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2002
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(02)00486-7