Eigenvalue computation for unitary rank 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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In this paper we describe how one can represent a unitary rank structured matrix in an efficient way as a product of unitary or Givens transformations. We provide also some basic operations for manipulating the representation, such as the transition to zerocreating form, the transition to a unitary/Givens-weight representation, as well as an internal pull-through process of the two branches of ...
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Let H ∈ Cn×n be an n × n unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition H as H = H11 H12 H21 H22 , (0.1) where H11 is its k×k leading principal submatrix; H22 is the complementary matrix of H11. In this paper, H is constructed uniquely when its eigenvalues and the eigenvalues of b H11 and b H22 are known. Here b H11 and b H22 are rank-one modifications of...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2008
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.01.006