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Volumn 29, Issue 2, 2007, Pages 413-433

A partial condition number for linear least squares problems

Author keywords

Linear least squares; Normwise condition number; Parameter estimation; Statistical condition estimate

Indexed keywords

COMPUTATIONAL METHODS; MATRIX ALGEBRA; NUMBER THEORY; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; VECTORS;

EID: 34948875289     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/050643088     Document Type: Article
Times cited : (36)

References (21)
  • 2
    • 0041412798 scopus 로고    scopus 로고
    • A subspace error estimate for linear systems
    • Y. CAO AND L. PETZOLD, A subspace error estimate for linear systems, SIAM J. Matrix Anal. Appl., 24 (2003), pp. 787-801.
    • (2003) SIAM J. Matrix Anal. Appl , vol.24 , pp. 787-801
    • CAO, Y.1    PETZOLD, L.2
  • 3
    • 42649119234 scopus 로고
    • On the sensitivity of solution components in linear systems of equations
    • S. CHANDRASEKARAN AND I. C. F. IPSEN, On the sensitivity of solution components in linear systems of equations, Numer. Linear Algebra Appl., 2 (1995), pp. 271-286.
    • (1995) Numer. Linear Algebra Appl , vol.2 , pp. 271-286
    • CHANDRASEKARAN, S.1    IPSEN, I.C.F.2
  • 4
    • 0001152877 scopus 로고
    • Perturbation theory for the least squares problem with linear equality constraints
    • L. ELDÉN, Perturbation theory for the least squares problem with linear equality constraints, SIAM J. Numer. Anal., 17 (1980), pp. 338-350.
    • (1980) SIAM J. Numer. Anal , vol.17 , pp. 338-350
    • ELDÉN, L.1
  • 5
    • 0043187360 scopus 로고    scopus 로고
    • Structured backward error and condition number for linear systems of the type A* Ax = b
    • V. FRAYSSÉ, S. GRATTON, AND V. TOUMAZOU, Structured backward error and condition number for linear systems of the type A* Ax = b, BIT, 40 (2000), pp. 74-83.
    • (2000) BIT , vol.40 , pp. 74-83
    • FRAYSSÉ, V.1    GRATTON, S.2    TOUMAZOU, V.3
  • 6
    • 0002205999 scopus 로고
    • A contribution to the theory of condition
    • A. J. GEURTS, A contribution to the theory of condition, Numer. Math., 39 (1982), pp. 85-96.
    • (1982) Numer. Math , vol.39 , pp. 85-96
    • GEURTS, A.J.1
  • 7
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed, The Johns Hopkins University Press, Baltimore, MD
    • G. GOLUB AND C. VAN LOAN, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore, MD, 1996.
    • (1996) Matrix Computations
    • GOLUB, G.1    VAN LOAN, C.2
  • 8
    • 0042224008 scopus 로고    scopus 로고
    • On the condition number of linear least squares problems in a weighted Frobenius norm
    • S. GRATTON, On the condition number of linear least squares problems in a weighted Frobenius norm, BIT, 36 (1996), pp. 523-530.
    • (1996) BIT , vol.36 , pp. 523-530
    • GRATTON, S.1
  • 9
    • 42649143930 scopus 로고    scopus 로고
    • Adjoint Formulas for Condition Numbers Applied to Linear and Indefinite Least Squares
    • Technical report LBNL-55221, Lawrence Berkeley National Laboratory
    • J. F. GRCAR, Adjoint Formulas for Condition Numbers Applied to Linear and Indefinite Least Squares, Technical report LBNL-55221, Lawrence Berkeley National Laboratory, 2005.
    • (2005)
    • GRCAR, J.F.1
  • 13
    • 0002565781 scopus 로고
    • Small-sample statistical condition estimates for general matrix functions
    • C. S. KENNEY AND A. J. LAUB, Small-sample statistical condition estimates for general matrix functions, SIAM J. Sei. Comput., 15 (1994), pp. 36-61.
    • (1994) SIAM J. Sei. Comput , vol.15 , pp. 36-61
    • KENNEY, C.S.1    LAUB, A.J.2
  • 14
    • 0032346187 scopus 로고    scopus 로고
    • Statistical condition estimation for linear least squares
    • C. S. KENNEY, A. J. LAUB, AND M. S. REESE, Statistical condition estimation for linear least squares, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 906-923.
    • (1998) SIAM J. Matrix Anal. Appl , vol.19 , pp. 906-923
    • KENNEY, C.S.1    LAUB, A.J.2    REESE, M.S.3
  • 15
    • 0001129014 scopus 로고
    • Towards a generalized singular value decomposition
    • C. C. PAIGE AND M. A. SAUNDERS, Towards a generalized singular value decomposition, SIAM J. Numer. Anal., 18 (1981), pp. 398-405.
    • (1981) SIAM J. Numer. Anal , vol.18 , pp. 398-405
    • PAIGE, C.C.1    SAUNDERS, M.A.2
  • 16
    • 0039943513 scopus 로고
    • LSQR: An algorithm for sparse linear equations and sparse least squares
    • C. C. PAIGE AND M. A. SAUNDERS, LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Software, 8 (1982), pp. 43-71.
    • (1982) ACM Trans. Math. Software , vol.8 , pp. 43-71
    • PAIGE, C.C.1    SAUNDERS, M.A.2
  • 19
    • 0016926423 scopus 로고
    • Generalizing the singular value decomposition
    • C. F. VAN LOAN, Generalizing the singular value decomposition, SIAM J. Numer. Anal., 13 (1976), pp. 76-83.
    • (1976) SIAM J. Numer. Anal , vol.13 , pp. 76-83
    • VAN LOAN, C.F.1
  • 20
    • 33344465568 scopus 로고    scopus 로고
    • Condition Number for Weighted Linear Least Squares Problem and Its Condition Number
    • 04-02-SQ, Department of Computing and Software, McMaster University, Hamilton, ON, Canada
    • Y. WEI, H. DIAO, AND S. QIAO, Condition Number for Weighted Linear Least Squares Problem and Its Condition Number, Technical report CAS 04-02-SQ, Department of Computing and Software, McMaster University, Hamilton, ON, Canada, 2004.
    • (2004) Technical report CAS
    • WEI, Y.1    DIAO, H.2    QIAO, S.3
  • 21
    • 42649115557 scopus 로고    scopus 로고
    • Componentwise Condition Numbers for Generalized Matrix Inversion and Linear Least Squares
    • 03-12-SQ, Department of Computing and Software, McMaster University, Hamilton, ON, Canada
    • Y. WEI, W. XU, S. QIAO, AND H. DIAO, Componentwise Condition Numbers for Generalized Matrix Inversion and Linear Least Squares, Technical report CAS 03-12-SQ, Department of Computing and Software, McMaster University, Hamilton, ON, Canada, 2003.
    • (2003) Technical report CAS
    • WEI, Y.1    XU, W.2    QIAO, S.3    DIAO, H.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.