메뉴 건너뛰기




Volumn 36, Issue 1, 1996, Pages 14-40

An algorithm and a stability theory for downdating the ULV decomposition

Author keywords

Downdating; Error analysis; Orthogonal decomposition; Subspaces

Indexed keywords


EID: 2542526304     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01740542     Document Type: Article
Times cited : (22)

References (25)
  • 1
    • 0021973363 scopus 로고
    • Stability analysis of the G-algorithm and a note on its application to sparse least squares problems
    • J. L. Barlow, Stability analysis of the G-algorithm and a note on its application to sparse least squares problems, BIT, 25 (1985), pp. 507-520.
    • (1985) BIT , vol.25 , pp. 507-520
    • Barlow, J.L.1
  • 2
    • 0025445384 scopus 로고
    • Computing accurate eigensystems of scaled diagonally dominant matrices
    • J. L. Barlow and J. W. Demmel, Computing accurate eigensystems of scaled diagonally dominant matrices, SIAM J. Numer. Anal., 27 (1990), pp. 762-791.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 762-791
    • Barlow, J.L.1    Demmel, J.W.2
  • 3
    • 0001659003 scopus 로고
    • The direct solution of weighted and equality constrained least squares problems
    • J. L. Barlow and S. L. Handy, The direct solution of weighted and equality constrained least squares problems, SIAM J. Sci. Stat. Computing, 9 (1988), pp. 704-716.
    • (1988) SIAM J. Sci. Stat. Computing , vol.9 , pp. 704-716
    • Barlow, J.L.1    Handy, S.L.2
  • 4
    • 85033753717 scopus 로고
    • An algorithm and a stability theory for downdating the ULV decomposition
    • Department of Computer Science and Engineering, The Pennsylvania State University, April
    • J. L. Barlow, P. A. Yoon, and H. Zha, An algorithm and a stability theory for downdating the ULV decomposition, Technical Report CSE-95-010, Department of Computer Science and Engineering, The Pennsylvania State University, April 1995.
    • (1995) Technical Report CSE-95-010
    • Barlow, J.L.1    Yoon, P.A.2    Zha, H.3
  • 5
    • 85033770802 scopus 로고
    • Efficient and stable algorithms for modifying the singular value decomposition and partial singular value decomposition
    • Technical Report CSE-93-19, Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA, September Submitted to
    • J. L. Barlow, H. Zha, and P. A. Yoon, Efficient and stable algorithms for modifying the singular value decomposition and partial singular value decomposition, Technical Report CSE-93-19, Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA, September 1993. Submitted to Numer. Math.
    • (1993) Numer. Math.
    • Barlow, J.L.1    Zha, H.2    Yoon, P.A.3
  • 6
    • 0002671024 scopus 로고
    • Stability analysis of the method of semi-normal equations for linear least squares problems
    • Å. Björck, Stability analysis of the method of semi-normal equations for linear least squares problems, Linear Algebra Appl., 88/89 (1987), pp. 31-48.
    • (1987) Linear Algebra Appl. , vol.88-89 , pp. 31-48
    • Björck, Å.1
  • 7
  • 8
    • 21144468781 scopus 로고
    • Jacobi's method is more accurate than QR
    • J. W. Demmel and K. Veselić, Jacobi's method is more accurate than QR, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 1204-1243.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 1204-1243
    • Demmel, J.W.1    Veselić, K.2
  • 10
    • 85033770162 scopus 로고    scopus 로고
    • Perturbation analysis of block downdating of a Cholesky decomposition
    • to appear
    • L. Eldén and H. Park, Perturbation analysis of block downdating of a Cholesky decomposition, Numer. Math., to appear.
    • Numer. Math.
    • Eldén, L.1    Park, H.2
  • 11
    • 85033741948 scopus 로고
    • Perturbation analysis for two-sided (or complete) orthogonal decompositions
    • Department of Mathematics, California State University, San Marcos, CA, February
    • R. D. Fierro, Perturbation analysis for two-sided (or complete) orthogonal decompositions, Technical Report 94-02, Department of Mathematics, California State University, San Marcos, CA, February 1994.
    • (1994) Technical Report 94-02
    • Fierro, R.D.1
  • 12
    • 0040654225 scopus 로고
    • Bounding the sub spaces from rank revealing two-sided orthogonal decompositions
    • Department of Mathematics, California State University, San Marcos, CA, May
    • R. D. Fierro and J.R. Bunch, Bounding the sub spaces from rank revealing two-sided orthogonal decompositions, Technical Report 94-05, Department of Mathematics, California State University, San Marcos, CA, May 1994.
    • (1994) Technical Report 94-05
    • Fierro, R.D.1    Bunch, J.R.2
  • 13
    • 85033766343 scopus 로고
    • Approximating the LS and TLS solutions by rank revealing two-sided orthogonal decomposition
    • Department of Mathematics, University of California at Los Angeles, Los Angeles, CA
    • R. D. Fierro and P. C. Hansen, Approximating the LS and TLS solutions by rank revealing two-sided orthogonal decomposition, Technical Report 93-16, Department of Mathematics, University of California at Los Angeles, Los Angeles, CA, 1993.
    • (1993) Technical Report 93-16
    • Fierro, R.D.1    Hansen, P.C.2
  • 14
    • 84966204836 scopus 로고
    • Methods for modifying matrix factorizations
    • P. E. Gill, G. H. Golub, W. Murray, and M. A. Saunders, Methods for modifying matrix factorizations, Math. Comp., 28 (1974), pp. 505-535.
    • (1974) Math. Comp. , vol.28 , pp. 505-535
    • Gill, P.E.1    Golub, G.H.2    Murray, W.3    Saunders, M.A.4
  • 17
    • 0040654213 scopus 로고
    • An efficient total least squares algorithm based on a rank revealing two-sided orthogonal decomposition
    • S. Van Huffel and H. Zha, An efficient total least squares algorithm based on a rank revealing two-sided orthogonal decomposition, Numerical Algorithms, 4 (1993), pp. 101-133.
    • (1993) Numerical Algorithms , vol.4 , pp. 101-133
    • Van Huffel, S.1    Zha, H.2
  • 20
    • 0002583762 scopus 로고
    • A modification to the LINPACK downdating algorithm
    • C.-T. Pan. A modification to the LINPACK downdating algorithm. BIT, 30:707-722, 1990.
    • (1990) BIT , vol.30 , pp. 707-722
    • Pan, C.-T.1
  • 21
    • 21144479924 scopus 로고
    • A perturbation analysis on the problem of downdating a Cholesky factorization
    • C.-T. Pan, A perturbation analysis on the problem of downdating a Cholesky factorization, Linear Algebra Appl., 183 (1993), pp. 103-115.
    • (1993) Linear Algebra Appl. , vol.183 , pp. 103-115
    • Pan, C.-T.1
  • 22
    • 21844500329 scopus 로고
    • Downdating the rank-revealing URV decomposition
    • H. Park and L. Eldén. Downdating the rank-revealing URV decomposition, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 138-156.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 138-156
    • Park, H.1    Eldén, L.2
  • 23
    • 0000672950 scopus 로고
    • The effects of rounding error on an algorithm for downdating a Cholesky factorization
    • G. W. Stewart, The effects of rounding error on an algorithm for downdating a Cholesky factorization, J. Inst. Maths. Applies., 23 (1979), pp. 203-213.
    • (1979) J. Inst. Maths. Applies. , vol.23 , pp. 203-213
    • Stewart, G.W.1
  • 24
    • 0040793105 scopus 로고
    • Two simple residual bounds for the eigenvalues of a Hermitian matrix
    • G. W. Stewart, Two simple residual bounds for the eigenvalues of a Hermitian matrix, SIAM J. Matrix Anal. Appl., 12 (1991), pp. 205-209.
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , pp. 205-209
    • Stewart, G.W.1
  • 25
    • 0040130684 scopus 로고
    • Updating a rank-revealing ULV decomposition
    • G. W. Stewart, Updating a rank-revealing ULV decomposition, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 494-499.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 494-499
    • Stewart, G.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.