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Volumn 215, Issue 1, 2008, Pages 49-78

Unitary rank structured matrices

Author keywords

Givens transformation; Pull through operation; Rank structured matrix; Shift correction term; Unitary matrix

Indexed keywords

MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS;

EID: 39849093448     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.03.020     Document Type: Article
Times cited : (5)

References (33)
  • 3
    • 84957527611 scopus 로고    scopus 로고
    • G.S. Ammar, W.B. Gragg, L. Reichel, Determination of Pisarenko frequency estimates as eigenvalues of an orthogonal matrix, in: F.T. Luk (Ed.), Proceedings of SPIE-The International Society for Optical Engineers, Advanced Algorithms and Architectures for Signal Processing II, California, SPIE, SPIE. Proceedings of SPIE-The International Society for Optical Engineering, vol. 826, SPIE, Bellingham, Washington, USA, 1987, pp. 143-145.
    • G.S. Ammar, W.B. Gragg, L. Reichel, Determination of Pisarenko frequency estimates as eigenvalues of an orthogonal matrix, in: F.T. Luk (Ed.), Proceedings of SPIE-The International Society for Optical Engineers, Advanced Algorithms and Architectures for Signal Processing II, California, SPIE, SPIE. Proceedings of SPIE-The International Society for Optical Engineering, vol. 826, SPIE, Bellingham, Washington, USA, 1987, pp. 143-145.
  • 4
    • 38249013559 scopus 로고
    • Downdating of Szego{combining double acute accent} polynomials and data-fitting applications
    • Ammar G.S., Gragg W.B., and Reichel L. Downdating of Szego{combining double acute accent} polynomials and data-fitting applications. Linear Algebra Appl. 172 (1992) 315-336
    • (1992) Linear Algebra Appl. , vol.172 , pp. 315-336
    • Ammar, G.S.1    Gragg, W.B.2    Reichel, L.3
  • 5
    • 0002931349 scopus 로고
    • On the spectral decomposition of hermitian matrices modified by low rank perturbations with applications
    • Arbenz P., and Golub G.H. On the spectral decomposition of hermitian matrices modified by low rank perturbations with applications. SIAM J. Matrix Anal. Appl. 9 1 (1988) 40-58
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , Issue.1 , pp. 40-58
    • Arbenz, P.1    Golub, G.H.2
  • 6
    • 39849093409 scopus 로고    scopus 로고
    • D. Bindel, S. Chandrasekaran, J.W. Demmel, D. Garmire, M. Gu, A fast and stable nonsymmetric eigensolver for certain structured matrices, Technical report, May 2005.
    • D. Bindel, S. Chandrasekaran, J.W. Demmel, D. Garmire, M. Gu, A fast and stable nonsymmetric eigensolver for certain structured matrices, Technical report, May 2005.
  • 7
    • 22744450946 scopus 로고    scopus 로고
    • On the shifted QR-iteration applied to Frobenius matrices
    • Bini D.A., Daddi F., and Gemignani L. On the shifted QR-iteration applied to Frobenius matrices. Electron. Trans. Numer. Anal. 18 (2004) 137-152
    • (2004) Electron. Trans. Numer. Anal. , vol.18 , pp. 137-152
    • Bini, D.A.1    Daddi, F.2    Gemignani, L.3
  • 8
    • 37249038818 scopus 로고    scopus 로고
    • Fast QR eigenvalue algorithms for Hessenberg matrices which are rank-one perturbations of unitary matrices
    • Bini D.A., Eidelman Y., Gemignani L., and Gohberg I.C. Fast QR eigenvalue algorithms for Hessenberg matrices which are rank-one perturbations of unitary matrices. SIAM J. Matrix Anal. Appl. 29 2 (2007) 566-585
    • (2007) SIAM J. Matrix Anal. Appl. , vol.29 , Issue.2 , pp. 566-585
    • Bini, D.A.1    Eidelman, Y.2    Gemignani, L.3    Gohberg, I.C.4
  • 9
    • 39849092525 scopus 로고    scopus 로고
    • D.A. Bini, L. Gemignani, V.Y. Pan, QR-like algorithms for generalized semiseparable matrices, Technical Report 1470, Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy, 2004.
    • D.A. Bini, L. Gemignani, V.Y. Pan, QR-like algorithms for generalized semiseparable matrices, Technical Report 1470, Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy, 2004.
  • 10
    • 21844489079 scopus 로고
    • Vector orthogonal polynomials and least squares approximation
    • Bultheel A., and Van Barel M. Vector orthogonal polynomials and least squares approximation. SIAM J. Matrix Anal. Appl. 16 3 (1995) 863-885
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , Issue.3 , pp. 863-885
    • Bultheel, A.1    Van Barel, M.2
  • 11
    • 39849098707 scopus 로고    scopus 로고
    • S. Chandrasekaran, M. Gu, J. Xia, J. Zhu, A fast QR algorithm for companion matrices, preprint 〈http://www.math.ucla.edu/~jxia/〉, 2006.
    • S. Chandrasekaran, M. Gu, J. Xia, J. Zhu, A fast QR algorithm for companion matrices, preprint 〈http://www.math.ucla.edu/~jxia/〉, 2006.
  • 12
    • 34547174625 scopus 로고    scopus 로고
    • Efficient implementation of the multishift QR algorithm for the unitary eigenvalue problem
    • David R.J.A., and Watkins D.S. Efficient implementation of the multishift QR algorithm for the unitary eigenvalue problem. SIAM J. Matrix Anal. Appl. 28 3 (2006) 623-633
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , Issue.3 , pp. 623-633
    • David, R.J.A.1    Watkins, D.S.2
  • 13
    • 39849106864 scopus 로고    scopus 로고
    • S. Delvaux, M. Van Barel, A Givens-weight representation for rank structured matrices, Technical Report TW453, Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3000 Leuven (Heverlee), Belgium, March 2006.
    • S. Delvaux, M. Van Barel, A Givens-weight representation for rank structured matrices, Technical Report TW453, Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3000 Leuven (Heverlee), Belgium, March 2006.
  • 14
    • 39849093254 scopus 로고    scopus 로고
    • S. Delvaux, M. Van Barel, A QR-based solver for rank structured matrices, Technical Report TW454, Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3000 Leuven (Heverlee), Belgium, March 2006.
    • S. Delvaux, M. Van Barel, A QR-based solver for rank structured matrices, Technical Report TW454, Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3000 Leuven (Heverlee), Belgium, March 2006.
  • 15
    • 31544452773 scopus 로고    scopus 로고
    • Rank structures preserved by the QR-algorithm: the singular case
    • Delvaux S., and Van Barel M. Rank structures preserved by the QR-algorithm: the singular case. J. Comput. Appl. Math. 189 (2006) 157-178
    • (2006) J. Comput. Appl. Math. , vol.189 , pp. 157-178
    • Delvaux, S.1    Van Barel, M.2
  • 16
    • 33847126104 scopus 로고    scopus 로고
    • Structures preserved by matrix inversion
    • Delvaux S., and Van Barel M. Structures preserved by matrix inversion. SIAM J. Matrix Anal. Appl. 28 1 (2006) 213-228
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , Issue.1 , pp. 213-228
    • Delvaux, S.1    Van Barel, M.2
  • 17
    • 37549005595 scopus 로고    scopus 로고
    • S. Delvaux, M. Van Barel, Eigenvalue computation for unitary rank structured matrices, J. Comput. Appl. Math. 2007, in press, doi: 10.1016/j.cam.2007.01.006.
    • S. Delvaux, M. Van Barel, Eigenvalue computation for unitary rank structured matrices, J. Comput. Appl. Math. 2007, in press, doi: 10.1016/j.cam.2007.01.006.
  • 18
    • 48249103929 scopus 로고    scopus 로고
    • S. Delvaux, M. Van Barel, A Hessenberg reduction algorithm for rank structured matrices, SIAM J. Matrix Anal. Appl. 2007, accepted for publication.
    • S. Delvaux, M. Van Barel, A Hessenberg reduction algorithm for rank structured matrices, SIAM J. Matrix Anal. Appl. 2007, accepted for publication.
  • 20
    • 0002755043 scopus 로고
    • Extensions of band matrices with band inverses
    • Dym H., and Gohberg I.C. Extensions of band matrices with band inverses. Linear Algebra Appl. 36 (1981) 1-24
    • (1981) Linear Algebra Appl. , vol.36 , pp. 1-24
    • Dym, H.1    Gohberg, I.C.2
  • 21
    • 31244431952 scopus 로고    scopus 로고
    • A modification of the Dewilde-van der Veen method for inversion of finite structured matrices
    • Eidelman Y., and Gohberg I.C. A modification of the Dewilde-van der Veen method for inversion of finite structured matrices. Linear Algebra Appl. 343-344 (2002) 419-450
    • (2002) Linear Algebra Appl. , vol.343-344 , pp. 419-450
    • Eidelman, Y.1    Gohberg, I.C.2
  • 22
    • 2542426782 scopus 로고
    • A note on extensions of band matrices with invertible maximal and submaximal blocks
    • Gohberg I.C., Kaashoek M.A., and Woerdeman H.J. A note on extensions of band matrices with invertible maximal and submaximal blocks. Linear Algebra Appl. 150 (1991) 157-166
    • (1991) Linear Algebra Appl. , vol.150 , pp. 157-166
    • Gohberg, I.C.1    Kaashoek, M.A.2    Woerdeman, H.J.3
  • 24
    • 38249042117 scopus 로고
    • The QR algorithm for unitary Hessenberg matrices
    • Gragg W.B. The QR algorithm for unitary Hessenberg matrices. J. Comput. Appl. Math. 16 (1986) 1-8
    • (1986) J. Comput. Appl. Math. , vol.16 , pp. 1-8
    • Gragg, W.B.1
  • 25
    • 84966200624 scopus 로고
    • Discrete least squares approximation by trigonometric polynomials
    • Reichel L., Ammar G.S., and Gragg W.B. Discrete least squares approximation by trigonometric polynomials. Math. Comput. 57 (1991) 273-289
    • (1991) Math. Comput. , vol.57 , pp. 273-289
    • Reichel, L.1    Ammar, G.S.2    Gragg, W.B.3
  • 26
    • 33847118509 scopus 로고    scopus 로고
    • An error analysis of a unitary Hessenberg QR algorithm
    • Stewart M. An error analysis of a unitary Hessenberg QR algorithm. SIAM J. Matrix Anal. Appl. 28 1 (2006) 40-67
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , Issue.1 , pp. 40-67
    • Stewart, M.1
  • 27
    • 21144472523 scopus 로고
    • A parallel algorithm for discrete least squares rational approximation
    • Van Barel M., and Bultheel A. A parallel algorithm for discrete least squares rational approximation. Numer. Math. 63 (1992) 99-121
    • (1992) Numer. Math. , vol.63 , pp. 99-121
    • Van Barel, M.1    Bultheel, A.2
  • 28
    • 0028423962 scopus 로고
    • Discrete linearized least squares approximation on the unit circle
    • Van Barel M., and Bultheel A. Discrete linearized least squares approximation on the unit circle. J. Comput. Appl. Math. 50 (1994) 545-563
    • (1994) J. Comput. Appl. Math. , vol.50 , pp. 545-563
    • Van Barel, M.1    Bultheel, A.2
  • 29
    • 0001844098 scopus 로고
    • Orthonormal polynomial vectors and least squares approximation for a discrete inner product
    • Van Barel M., and Bultheel A. Orthonormal polynomial vectors and least squares approximation for a discrete inner product. Electron. Trans. Numer. Anal. 3 (1995) 1-23
    • (1995) Electron. Trans. Numer. Anal. , vol.3 , pp. 1-23
    • Van Barel, M.1    Bultheel, A.2
  • 30
    • 26644435288 scopus 로고    scopus 로고
    • A note on the representation and definition of semiseparable matrices
    • Vandebril R., Van Barel M., and Mastronardi N. A note on the representation and definition of semiseparable matrices. Numer. Linear Algebra Appl. 12 8 (2005) 839-858
    • (2005) Numer. Linear Algebra Appl. , vol.12 , Issue.8 , pp. 839-858
    • Vandebril, R.1    Van Barel, M.2    Mastronardi, N.3
  • 31
    • 0036790288 scopus 로고    scopus 로고
    • Convergence of the shifted QR algorithm, for unitary Hessenberg matrices
    • Wang T.L., and Gragg W.B. Convergence of the shifted QR algorithm, for unitary Hessenberg matrices. Math. Comput. 71 240 (2002) 1473-1496
    • (2002) Math. Comput. , vol.71 , Issue.240 , pp. 1473-1496
    • Wang, T.L.1    Gragg, W.B.2
  • 32
    • 0037232526 scopus 로고    scopus 로고
    • Convergence of the unitary QR algorithm with unitary Wilkinson shift
    • Wang T.L., and Gragg W.B. Convergence of the unitary QR algorithm with unitary Wilkinson shift. Math. Comput. 72 241 (2003) 375-385
    • (2003) Math. Comput. , vol.72 , Issue.241 , pp. 375-385
    • Wang, T.L.1    Gragg, W.B.2
  • 33
    • 39849092209 scopus 로고    scopus 로고
    • H.J. Woerdeman, Matrix and operator extensions, CWI Tract, vol. 68, Centre for Mathematics and Computer Science, Amsterdam, 1989.
    • H.J. Woerdeman, Matrix and operator extensions, CWI Tract, vol. 68, Centre for Mathematics and Computer Science, Amsterdam, 1989.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.