메뉴 건너뛰기




Volumn 24, Issue 4, 2003, Pages 1186-1196

A unified theory of conditioning for linear least squares and Tikhonov regularization solutions

Author keywords

Condition number; Constrained least squares; Tikhonov regularization

Indexed keywords


EID: 0142138703     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479801389564     Document Type: Article
Times cited : (22)

References (11)
  • 2
    • 0000355024 scopus 로고
    • Norm-preserving dilations and their applications to optimal error bounds
    • C. DAVIS, W.M. KAHAN, AND H.F. WEINBERGER, Norm-preserving dilations and their applications to optimal error bounds, SIAM J. Numer. Anal., 19 (1982), pp. 445-469.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 445-469
    • Davis, C.1    Kahan, W.M.2    Weinberger, H.F.3
  • 3
    • 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
  • 4
    • 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
  • 5
    • 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
  • 6
    • 0034419754 scopus 로고    scopus 로고
    • Perturbation theory for generalized and constrained linear least squares
    • M. GULLIKSSON AND P.-A. WEDIN, Perturbation theory for generalized and constrained linear least squares, Numer. Linear Algebra Appl., 7 (2000), pp. 181-195.
    • (2000) Numer. Linear Algebra Appl. , vol.7 , pp. 181-195
    • Gulliksson, M.1    Wedin, P.-A.2
  • 7
    • 0011120580 scopus 로고    scopus 로고
    • Perturbation identities for regularized Tikhonov inverses and weighted pseudoinverses
    • M.E. GULLIKSSON, P.-A. WEDIN, AND Y. WEI, Perturbation identities for regularized Tikhonov inverses and weighted pseudoinverses, BIT, 40 (2000), pp. 513-523.
    • (2000) BIT , vol.40 , pp. 513-523
    • Gulliksson, M.E.1    Wedin, P.-A.2    Wei, Y.3
  • 8
    • 0000374864 scopus 로고
    • Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank
    • P.C. HANSEN, Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank, SIAM J. Sci. Stat. Comput., 11 (1990), pp. 503-518.
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , pp. 503-518
    • Hansen, P.C.1
  • 9
    • 0035658120 scopus 로고    scopus 로고
    • Computation of Lagrange multipliers for linear least squares problems with equality constraints
    • A. LARATTA AND F. ZIRONI, Computation of Lagrange multipliers for linear least squares problems with equality constraints, Computing, 67 (2001), pp. 335-350.
    • (2001) Computing , vol.67 , pp. 335-350
    • Laratta, A.1    Zironi, F.2
  • 10
    • 0000303960 scopus 로고
    • A theory of condition
    • J.R. RICE, A theory of condition, SIAM J. Numer. Anal., 3 (1966), pp. 287-310.
    • (1966) SIAM J. Numer. Anal. , vol.3 , pp. 287-310
    • Rice, J.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.