메뉴 건너뛰기




Volumn 94, Issue 2, 2003, Pages 203-228

Multi-parameter regularization techniques for ill-conditioned linear systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0142023207     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-002-0435-8     Document Type: Article
Times cited : (81)

References (29)
  • 7
    • 0034419035 scopus 로고    scopus 로고
    • On a variational formulation of the QSVD and the RSVD
    • D. Chu, B. De Moor: On a variational formulation of the QSVD and the RSVD. Linear Algebra Appl., 311, 61-78 (2000)
    • (2000) Linear Algebra Appl. , vol.311 , pp. 61-78
    • Chu, D.1    De Moor, B.2
  • 8
    • 34250263445 scopus 로고
    • Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of Generalized Cross Validation
    • P. Craven, G. Wahba: Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of Generalized Cross Validation. Numer. Math., 31, 377-403 (1979)
    • (1979) Numer. Math. , vol.31 , pp. 377-403
    • Craven, P.1    Wahba, G.2
  • 9
    • 0142113775 scopus 로고
    • Generalizations of the singular value and Q R-decompositions
    • B. De Moor, P. Van Dooren: Generalizations of the singular value and Q R-decompositions. SIAM J. Matrix Anal. Appl., 13, 993-1014 (1992)
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 993-1014
    • De Moor, B.1    Van Dooren, P.2
  • 10
    • 0040802669 scopus 로고
    • A tree of generalizations of the ordinary singular value decomposition
    • B. De Moor, H.Y. Zha: A tree of generalizations of the ordinary singular value decomposition. Linear Algebra Appl., 147, 469-500 (1991)
    • (1991) Linear Algebra Appl. , vol.147 , pp. 469-500
    • De Moor, B.1    Zha, H.Y.2
  • 11
    • 0006603056 scopus 로고
    • The restricted singular value decomposition: Properties and applications
    • B.L.R. De Moor, G.H. Golub: The restricted singular value decomposition: properties and applications. SIAM J. Matrix Anal. Appl., 12, 401-425 (1991)
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , pp. 401-425
    • De Moor, B.L.R.1    Golub, G.H.2
  • 13
    • 0004236492 scopus 로고    scopus 로고
    • The John Hopkins University Press, Baltimore, 3rd edition
    • G.H. Golub, C.F. Van Loan: Matrix Computations. The John Hopkins University Press, Baltimore, 3rd edition, 1996
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 14
    • 0003368014 scopus 로고
    • The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind
    • Pitman, London
    • Ch.W. Groetsch: The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, volume 10 of Research Notes in Mathematics. Pitman, London, 1984
    • (1984) Research Notes in Mathematics , vol.10
    • Groetsch, Ch.W.1
  • 15
    • 0038992806 scopus 로고
    • Some properties of the regularized solutions of ill-conditioned linear systems
    • L. Guerri, S. Seatzu: Some properties of the regularized solutions of ill-conditioned linear systems. Boll. Unione Mat. Ital., VI Ser., B, 3, 435-450 (1984)
    • (1984) Boll. Unione Mat. Ital., VI Ser., B , vol.3 , pp. 435-450
    • Guerri, L.1    Seatzu, S.2
  • 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, 561-580 (1992)
    • (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, 1-35 (1994)
    • (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, D.P. O'Leary: The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput., 14, 1487-1503 (1993)
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1487-1503
    • Hansen, P.C.1    O'Leary, D.P.2
  • 21
    • 0003859364 scopus 로고    scopus 로고
    • South Natick, MA
    • The MathWorks Inc., South Natick, MA. MATLAB Version 6.1, 2001
    • (2001) MATLAB Version 6.1
  • 22
    • 0002902522 scopus 로고
    • Least squares methods for ill-posed problems with a prescribed bound
    • K. Miller: Least squares methods for ill-posed problems with a prescribed bound. J. Math. Anal., 1, 52-74 (1970)
    • (1970) J. Math. Anal. , vol.1 , pp. 52-74
    • Miller, K.1
  • 23
    • 0040176984 scopus 로고
    • The choice of parameter when solving functional equations by regularization
    • V.A. Morozov: The choice of parameter when solving functional equations by regularization. Dokl. Akad. Nauk SSSR, 175, 1225-1228 (1962)
    • (1962) Dokl. Akad. Nauk SSSR , vol.175 , pp. 1225-1228
    • Morozov, V.A.1
  • 24
    • 0001300995 scopus 로고
    • Regularization of incorrectly posed problems
    • A.N. Tikhonov: Regularization of incorrectly posed problems. Soviet Math. Dokl., 4, 1624-1627 (1963)
    • (1963) Soviet Math. Dokl. , vol.4 , pp. 1624-1627
    • Tikhonov, A.N.1
  • 25
    • 0001300994 scopus 로고
    • Solution of incorrectly formulated problems and the regularization method
    • A.N. Tikhonov: Solution of incorrectly formulated problems and the regularization method. Soviet Math, Dokl., 4, 1036-1038 (1963)
    • (1963) Soviet Math, Dokl. , vol.4 , pp. 1036-1038
    • Tikhonov, A.N.1
  • 29
    • 0000565140 scopus 로고
    • The restricted singular value decomposition of matrix triplets
    • H.Y. Zha: The restricted singular value decomposition of matrix triplets. SIAM J. Matrix Anal. Appl., 12, 172-194 (1991)
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , pp. 172-194
    • Zha, H.Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.