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Volumn 27, Issue 3, 2005, Pages 861-875

Core problems in linear algebraic systems

Author keywords

Bidiagonalization; Core problem; Data least squares; Ill posed problems; Least squares; Minimum 2 norm solutions; Orthogonal reduction; Orthogonal regression; Scaled total least squares; Singular value decomposition

Indexed keywords

LEAST SQUARES APPROXIMATIONS; LINEAR SYSTEMS; MATHEMATICAL MODELS; NUMBER THEORY; PROBLEM SOLVING;

EID: 33746132377     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/040616991     Document Type: Article
Times cited : (40)

References (28)
  • 2
    • 0001765884 scopus 로고
    • An implicit shift bidiagonalization algorithm for ill-posed problems
    • A. BJÖRCK, E. GRIMME, AND P. VAN DOOREN, An implicit shift bidiagonalization algorithm for ill-posed problems, BIT, 34 (1994), pp. 510-534.
    • (1994) BIT , vol.34 , pp. 510-534
    • Björck, A.1    Grimme, E.2    Van Dooren, P.3
  • 3
    • 2342524089 scopus 로고    scopus 로고
    • Partial least-squares us. Lanczos bidiagonalization-I: Analysis of a projection method for multiple regression
    • L. ELDÉN, Partial least-squares us. Lanczos bidiagonalization-I: Analysis of a projection method for multiple regression, Comput. Statist. Data Anal., 46 (2004), pp. 11-31.
    • (2004) Comput. Statist. Data Anal. , vol.46 , pp. 11-31
    • Eldén, L.1
  • 4
    • 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
  • 5
    • 9644257201 scopus 로고    scopus 로고
    • Perturbation theory for orthogonal projection methods with applications to least squares and total least squares
    • R. D. FIERRO AND J. R. BUNCH, Perturbation theory for orthogonal projection methods with applications 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
  • 7
    • 0001070999 scopus 로고
    • Some modified matrix eigenvalue problems
    • G. H. GOLUB, Some modified matrix eigenvalue problems, SIAM Rev., 15 (1973), pp. 318-334.
    • (1973) SIAM Rev. , vol.15 , pp. 318-334
    • Golub, G.H.1
  • 9
    • 45949115772 scopus 로고
    • A generalization of the Eckart-Young-Mirsky matrix approximation theorem
    • G. H. GOLUB, A. HOFFMAN, AND G. W. STEWART, A generalization of the Eckart-Young-Mirsky matrix approximation theorem, Linear Algebra Appl., 88/89 (1987), pp. 317-337.
    • (1987) Linear Algebra Appl. , vol.88-89 , pp. 317-337
    • Golub, G.H.1    Hoffman, A.2    Stewart, G.W.3
  • 10
    • 33747738463 scopus 로고
    • Singular value decomposition and least squares solutions
    • G. H. GOLUB AND C. REINSCH, Singular value decomposition and least squares solutions, Numer. Math., 14 (1970), pp. 403-420.
    • (1970) Numer. Math. , vol.14 , pp. 403-420
    • Golub, G.H.1    Reinsch, C.2
  • 11
    • 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
  • 13
    • 0027287116 scopus 로고
    • The data least squares problem and channel equalization
    • R. D. D. GROAT AND E. M. DOWLING, The data least squares problem and channel equalization, IEEE Trans. Signal Process., 42 (1993), pp. 407-411.
    • (1993) IEEE Trans. Signal Process. , vol.42 , pp. 407-411
    • Groat, R.D.D.1    Dowling, E.M.2
  • 14
    • 2942633674 scopus 로고    scopus 로고
    • On Lanczos based methods for the regularization of discrete ill-posed problems
    • M. HANKE, On Lanczos based methods for the regularization of discrete ill-posed problems, BIT, 41 (2001), pp. 1008-1018.
    • (2001) BIT , vol.41 , pp. 1008-1018
    • Hanke, M.1
  • 15
    • 0003235719 scopus 로고    scopus 로고
    • Rank-deficient and discrete ill-posed problems: Numerical aspects of linear inversion
    • SIAM, Philadelphia
    • P. C. HANSEN, Rank-Deficient and Discrete Ill-Posed problems: Numerical Aspects of Linear Inversion, SIAM Monogr. Math. Model, Comput. 4, SIAM, Philadelphia, 1997.
    • (1997) SIAM Monogr. Math. Model, Comput. , vol.4
    • Hansen, P.C.1
  • 16
    • 0000752748 scopus 로고
    • The modified truncated SVD method for regularization in general form
    • P. C. HANSEN, T. SEKII, AND H. SHIBAHASHI, The modified truncated SVD method for regularization in general form, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 1142-1150.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 1142-1150
    • Hansen, P.C.1    Sekii, T.2    Shibahashi, H.3
  • 18
    • 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, SLAM J. Sci. Statist. Comput., 2 (1981), pp. 474-489.
    • (1981) SLAM J. Sci. Statist. Comput. , vol.2 , pp. 474-489
    • O'Leary, D.P.1    Simmons, J.A.2
  • 19
    • 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
  • 20
    • 0036013504 scopus 로고    scopus 로고
    • Scaled total least squares fundamentals
    • C. C. PAIGE AND Z. STRAKOŠ, Scaled total least squares fundamentals, Numer. Math., 91 (2002), pp. 117-146.
    • (2002) Numer. Math. , vol.91 , pp. 117-146
    • Paige, C.C.1    Strakoš, Z.2
  • 21
    • 2942694426 scopus 로고    scopus 로고
    • Unifying least squares, total least squares and data least squares
    • S. van Huffel and P. Lemmerling, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands
    • C. C. PAIGB AND Z. STRAKOŠ, Unifying least squares, total least squares and data least squares, In Total Least Squares and Errors-in-Variables Modeling, S. van Huffel and P. Lemmerling, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002, pp. 35-34.
    • (2002) Total Least Squares and Errors-in-variables Modeling , pp. 35-134
    • Paigb, C.C.1    Strakoš, Z.2
  • 22
    • 0003128308 scopus 로고    scopus 로고
    • Unified treatment of LS, TLS, and truncated SVD methods using a weighted TLS framework
    • S. Van Huffel, ed., SIAM, Philadelphia
    • B. D. RAO, Unified treatment of LS, TLS, and truncated SVD methods using a weighted TLS framework, In Recent Advances In Total Least Squares Techniques and Errors-in-Variables Modelling, S. Van Huffel, ed., SIAM, Philadelphia, 1997, pp. 11-20.
    • (1997) Recent Advances in Total Least Squares Techniques and Errors-in-variables Modelling , pp. 11-20
    • Rao, B.D.1
  • 23
    • 34250412349 scopus 로고
    • Stability of the solutions of linear least squares problems
    • A. VAN DER SLUIS, Stability of the solutions of linear least squares problems, Numer. Math., 23 (1975), pp. 341-254.
    • (1975) Numer. Math. , vol.23 , pp. 341-1254
    • Van Der Sluis, A.1
  • 24
    • 9644307046 scopus 로고
    • Restoring rank and consistency by orthogonal projection
    • A. VAN DER SLUIS AND G. W. VELTKAMP, Restoring rank and consistency by orthogonal projection, Linear Algebra Appl., 28 (1979), pp. 257-278.
    • (1979) Linear Algebra Appl. , vol.28 , pp. 257-278
    • Van Der Sluis, A.1    Veltkamp, G.W.2
  • 25
    • 0003297912 scopus 로고
    • The total least squares problem: Computational aspects and analysis
    • SIAM, Philadelphia
    • S. VAN HUFFEL AND J. VANDEWALLE, The Total Least Squares Problem: Computational Aspects and Analysis, Frontiers Appl. Math. 9, SIAM, Philadelphia, 1991.
    • (1991) Frontiers Appl. Math. , vol.9
    • Van Huffel, S.1    Vandewalle, J.2
  • 27
    • 0001681052 scopus 로고
    • The collinearity problem in linear regression. the partial least squares (PLS) approach to generalised inverses
    • S. WOLD, A. RUHE, H. WOLD, AND W. J. DUNN, III, The collinearity problem in linear regression. The partial least squares (PLS) approach to generalised inverses, SIAM J. Sci. Statist. Comput., 5 (1984), pp. 735-743.
    • (1984) SIAM J. Sci. Statist. Comput. , vol.5 , pp. 735-743
    • Wold, S.1    Ruhe, A.2    Wold, H.3    Dunn III, W.J.4
  • 28
    • 0025477263 scopus 로고
    • Strong consistency of estimates made by the method of orthogonal projections
    • A. I. ZHDANOV AND O. A. KATSYUBA, Strong consistency of estimates made by the method of orthogonal projections, Internat, J. Systems 3d., 21 (1990), pp. 1463-1471.
    • (1990) Internat, J. Systems 3d. , vol.21 , pp. 1463-1471
    • Zhdanov, A.I.1    Katsyuba, O.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.