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Volumn 18, Issue 4, 1997, Pages 1223-1241

Regularization by truncated total least squares

Author keywords

Bidiagonalization; Discrete ill posed problems; Regularization; Total least squares

Indexed keywords

BIDIAGONALIZATION; COEFFICIENT MATRIX; DISCRETE ILL POSED PROBLEMS; REGULARIZATION; TRUNCATED TOTAL LEAST SQUARES;

EID: 0031173551     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827594263837     Document Type: Article
Times cited : (185)

References (30)
  • 1
    • 34250270918 scopus 로고
    • Updating the singular value decomposition
    • J. R. BUNCH AND C. P. NIELSEN, Updating the singular value decomposition, Numer. Math., 31 (1978), pp. 111-129.
    • (1978) Numer. Math. , vol.31 , pp. 111-129
    • Bunch, J.R.1    Nielsen, C.P.2
  • 2
    • 0001326391 scopus 로고
    • Some applications of the rank revealing QR factorization
    • T. F. CHAN AND P. C. HANSEN, Some applications of the rank revealing QR factorization, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 727-741.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 727-741
    • Chan, T.F.1    Hansen, P.C.2
  • 4
    • 0020243342 scopus 로고
    • A weighted pseudoinverse, generalized singular values, and constrained least squares problems
    • L. ELDÉN, A weighted pseudoinverse, generalized singular values, and constrained least squares problems, BIT, 22 (1982), pp. 487-502.
    • (1982) BIT , vol.22 , pp. 487-502
    • Eldén, L.1
  • 5
    • 21844488674 scopus 로고
    • Collinearity and total least squares
    • R. D. FIERRO AND J. R. BUNCH, Collinearity and total least squares, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 1167-1181.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 1167-1181
    • Fierro, R.D.1    Bunch, J.R.2
  • 6
    • 9644257201 scopus 로고    scopus 로고
    • Perturbation theory for orthogonal projection methods with application to least squares and total least squares
    • R. D. FIERRO AND J. R. BUNCH, Perturbation theory for orthogonal projection methods with application to least squares and total least squares, Linear Algebra Appl., 234 (1996), pp. 71-96.
    • (1996) Linear Algebra Appl. , vol.234 , pp. 71-96
    • Fierro, R.D.1    Bunch, J.R.2
  • 8
    • 32044449925 scopus 로고
    • Generalized cross-validation as a method for choosing a good ridge parameter
    • G. H. GOLUB, M. T. HEATH, AND G. WAHBA, Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics, 21 (1979), pp. 215-223.
    • (1979) Technometrics , vol.21 , pp. 215-223
    • Golub, G.H.1    Heath, M.T.2    Wahba, G.3
  • 9
    • 0000288016 scopus 로고
    • Calculating the singular values and pseudo-inverse of a matrix
    • Series B
    • G. H. GOLUB AND W. KAHAN, Calculating the singular values and pseudo-inverse of a matrix, SIAM J. Numer. Anal., 2 (Series B) (1965), pp. 205-224.
    • (1965) SIAM J. Numer. Anal. , vol.2 , pp. 205-224
    • Golub, G.H.1    Kahan, W.2
  • 10
    • 0000333571 scopus 로고
    • An analysis of the total least squares problem
    • G. H. GOLUB AND C. F. VAN LOAN, An analysis of the total least squares problem, SIAM J. Numer. Anal., 17 (1980), pp. 883-893.
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 883-893
    • Golub, G.H.1    Van Loan, C.F.2
  • 11
    • 0000223746 scopus 로고
    • Calculation of Gauss quadrature rules
    • G. GOLUB AND J. WELSCH, Calculation of Gauss quadrature rules, Math. Comp., 23 (1969), pp. 221-230.
    • (1969) Math. Comp. , vol.23 , pp. 221-230
    • Golub, G.1    Welsch, J.2
  • 13
    • 0001273835 scopus 로고
    • Regularization methods for large-scale problems
    • M. HANKE AND P. C. HANSEN, Regularization methods for large-scale problems, Surveys Math. Indust., 3 (1993), pp. 253-315.
    • (1993) Surveys Math. Indust. , vol.3 , pp. 253-315
    • Hanke, M.1    Hansen, P.C.2
  • 14
    • 0000303746 scopus 로고
    • Regularization, GSVD and truncated GSVD
    • P. C. HANSEN, Regularization, GSVD and truncated GSVD, BIT, 29 (1989), pp. 491-504.
    • (1989) BIT , vol.29 , pp. 491-504
    • Hansen, P.C.1
  • 15
    • 0000374864 scopus 로고
    • Truncated SVD solutions to discrete ill-posed problems with ill-determined numerical rank
    • P. C. HANSEN, Truncated SVD solutions to discrete ill-posed problems with ill-determined numerical rank, SIAM J. Sci. Statist. Comput., 11 (1990), pp. 503-518.
    • (1990) SIAM J. Sci. Statist. Comput. , vol.11 , pp. 503-518
    • Hansen, P.C.1
  • 16
    • 0000570697 scopus 로고
    • Analysis of discrete ill-posed problems by means of the L-curve
    • P. C. HANSEN, Analysis of discrete ill-posed problems by means of the L-curve, SIAM Rev., 34 (1992), pp. 561-580.
    • (1992) SIAM Rev. , vol.34 , pp. 561-580
    • Hansen, P.C.1
  • 17
    • 13344267706 scopus 로고
    • Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
    • P. C. HANSEN, Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems, Numer. Algorithms, 6 (1994), pp. 1-35.
    • (1994) Numer. Algorithms , vol.6 , pp. 1-35
    • Hansen, P.C.1
  • 18
    • 0001632418 scopus 로고
    • The. use of the L-curve in the regularization of discrete ill-posed problems
    • P. C. HANSEN AND D. P. O'LEARY, The. use of the L-curve in the regularization of discrete ill-posed problems, SIAM J. Sci. Comput., 14 (1993), pp. 1487-1503.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1487-1503
    • Hansen, P.C.1    O'Leary, D.P.2
  • 19
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • M. R. HESTENES AND E. STIEFEL, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bureau Standards, 49 (1952), pp. 409-436.
    • (1952) J. Res. Nat. Bureau Standards , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.2
  • 20
    • 0001452365 scopus 로고
    • A bidiagonalization-regularization procedure for large scale discretizations of ill-posed problems
    • D. P. O'LEARY AND J. A. SIMMONS, A bidiagonalization-regularization procedure for large scale discretizations of ill-posed problems, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 474-489.
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 474-489
    • O'Leary, D.P.1    Simmons, J.A.2
  • 21
    • 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
  • 22
    • 0004073954 scopus 로고
    • American Mathematical Society, Providence, RI
    • G. SZEGÖ, Orthogonal Polynomials, American Mathematical Society, Providence, RI, 1939.
    • (1939) Orthogonal Polynomials
    • Szegö, G.1
  • 23
    • 0001918839 scopus 로고
    • On the invariance of perturbed null vectors under column scaling
    • G. W. STEWART, On the invariance of perturbed null vectors under column scaling, Numer. Math., 44 (1984), pp. 61-65.
    • (1984) Numer. Math. , vol.44 , pp. 61-65
    • Stewart, G.W.1
  • 24
    • 6244257332 scopus 로고
    • Algebraic relationships between classical regression and total least-squares estimation
    • S. VAN HUFFEL AND J. VANDEWALLE, Algebraic relationships between classical regression and total least-squares estimation, Linear Algebra Appl., 93 (1987), pp. 149-162.
    • (1987) Linear Algebra Appl. , vol.93 , pp. 149-162
    • Van Huffel, S.1    Vandewalle, J.2
  • 25
    • 0346784009 scopus 로고
    • Analysis and solution of the nongeneric total least squares problem
    • S. VAN HUFFEL AND J. VANDEWALLE, Analysis and solution of the nongeneric total least squares problem, SIAM J. Matrix Anal. Appl., 9 (1988), pp. 327-348.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 327-348
    • Van Huffel, S.1    Vandewalle, J.2
  • 27
    • 38249035548 scopus 로고
    • An efficient and reliable algorithm for computing the singular subspace of a matrix, associated with its smallest singular values
    • S. VAN HUFFEL, J. VANDEWALLE, AND A. HAEGEMANS, An efficient and reliable algorithm for computing the singular subspace of a matrix, associated with its smallest singular values, J. Comput. Appl. Math., 19 (1987), pp. 313-330.
    • (1987) J. Comput. Appl. Math. , vol.19 , pp. 313-330
    • Van Huffel, S.1    Vandewalle, J.2    Haegemans, A.3
  • 28
    • 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, Numer. Algorithms, 4 (1993), pp. 101-133.
    • (1993) Numer. Algorithms , vol.4 , pp. 101-133
    • Van Huffel, S.1    Zha, H.2
  • 29
    • 0042906448 scopus 로고
    • The analysis for the total least squares problem with more than one solution
    • M. WEI, The analysis for the total least squares problem with more than one solution, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 746-763.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 746-763
    • Wei, M.1
  • 30
    • 34249843231 scopus 로고
    • Algebraic relations between the total least squares and least squares problems with more than one solution
    • M. WEI, Algebraic relations between the total least squares and least squares problems with more than one solution, Numer. Math., 62 (1992), pp. 123-148.
    • (1992) Numer. Math. , vol.62 , pp. 123-148
    • Wei, M.1


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