منابع مشابه
Structures preserved by the QR-algorithm
In this talk we investigate some classes of structures that are preserved by applying a QR step on a matrix A. We will handle two classes of such structures: the first we call polynomial structures, for example a matrix being Hermitian or Hermitian up to a rank one correction, and the second we call rank structures, which are encountered for example in all kinds of what we could call Hessenberg...
متن کاملRank structures preserved by the QR-algorithm: the singular case
In an earlier paper we introduced the classes of polynomial and rank structures, both of them preserved by applying a (shifted) QRstep on a matrix A. In the present paper we will further investigate the case of rank structures. We will show that even if A is a singular matrix, a new QR-iterate can be constructed having the same rank structure as the matrix A itself. To this end we will introduc...
متن کاملThe Periodic QR Algorithm is a Disguised QR Algorithm
Abstract The periodic QR algorithm is a strongly backward stable method for computing the eigenvalues of products of matrices, or equivalently for computing the eigenvalues of block cyclic matrices. The main purpose of this paper is to show that this algorithm is numerically equivalent to the standard QR algorithm. It will be demonstrated how this connection may be used to develop a better unde...
متن کاملStructures Preserved by Schur Complementation
In this paper we investigate some matrix structures on C that have a good behaviour under Schur complementation. The first type of structure is closely related to low displacement rank matrices. Next, we show that for a matrix having a low rank submatrix, also the Schur complement must have a low rank submatrix, which we can explicitly determine. This property holds even if the low rank submatr...
متن کاملStructures preserved by matrix inversion
Department of Computer Science, K.U.Leuven Celestijnenlaan 200A B-3001 Heverlee, Belgium In this talk we investigate some matrix structures on Cn×n that have a good behaviour under matrix inversion. The first kind of structure is strongly related to low displacement rank structure. The second kind of structure deals with certain low rank submatrices. In this case, it can be shown that also the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2006
ISSN: 0377-0427
DOI: 10.1016/j.cam.2005.03.028