Structures preserved by the QR-algorithm

Journal of Computational and Applied Mathematics

Volumn 187, Issue 1, 2006, Pages 29-40

  Delvaux, Steven ^a   Van Barel, Marc ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

(Shifted) QR algorithm; Hessenberg like matrices; Lower semiseparable like matrices; Polynomial structure; Rank structure

Indexed keywords

MATRIX ALGEBRA; POLYNOMIALS; STRUCTURAL ANALYSIS;

(SHIFTED) QR-ALGORITHM; HESSENBERG-LIKE MATRICES; LOWER SEMISEPARABLE-LIKE MATRICES; POLYNOMIAL STRUCTURE; RANK STRUCTURE;

ALGORITHMS;

EID: 27344459494     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.03.028     Document Type: Article

References (10)

1. P. Arbenz, and G.H. Golub Matrix shapes invariant under the symmetric QR algorithm Numer. Linear Algebra Appl. 2 2 1995 87 93
2. D.A. Bini, F. Daddi, and L. Gemignani On the shifted QR-iteration applied to Frobenius matrices Electron. Trans. Numer. Anal. 18 2004 137 152
3. D.A. Bini, L. Gemignani, V. Pan, QR-like algorithms for generalized semiseparable matrices, Technical Report 1470, Department of Mathematics, University of Pisa, 2004.
4. S. Delvaux, M. Van Barel, Rank structures preserved by the QR-algorithm: the singular case, Report TW 400, Department of Computer Science, K.U. Leuven, Leuven, Belgium, August 2004, J. Comput. Appl. Math., doi: 10.1016/j.cam.2005. 03.027.
5. D. Fasino, Rational Krylov matrices and QR-steps on Hermitian diagonal-plus-semiseparable matrices, Numer. Linear Algebra Appl. (2004), to appear, url: ftp://ftp.dimi.uniud.it/pub/fasino/bari.ps
6. L. Gemignani, A unitary Hessenberg QR-based algorithm via semiseparable matrices, url: www.dm.unipi.it/~gemignan/papers/unihess.pdf
7. G.H. Golub, and C.F. Van Loan Matrix Computations third ed. 1996 Johns Hopkins University Press Baltimore, MD
8. W.B. Gragg The QR algorithm for unitary Hessenberg matrices J. Comput. Appl. Math. 16 1986 1 8
9. M. Van Barel, R. Vandebril, N. Mastronardi, The Lanczos-Ritz values appearing in an orthogonal similarity reduction of a matrix into semiseparable form, Report TW 360, Department of Computer Science, K.U. Leuven, Leuven, Belgium, May 2003.
10. R. Vandebril, M. Van Barel, N. Mastronardi, An implicit QR algorithm for semiseparable matrices to compute the eigendecomposition of symmetric matrices, Report TW 367, Department of Computer Science, K.U. Leuven, Leuven, Belgium, August 2003.