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Volumn 43, Issue 4, 2002, Pages 359-373

The triangle method for finding the corner of the L-curve

Author keywords

CG method; Ill conditioned matrices; L curve; Regularization; Systems of linear equations

Indexed keywords

ERROR ANALYSIS; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; MATRIX ALGEBRA; OPTIMIZATION;

EID: 0036895160     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(01)00179-9     Document Type: Article
Times cited : (115)

References (18)
  • 1
    • 0041192970 scopus 로고    scopus 로고
    • Stability of conjugate gradient and lanczos methods for linear least squares problems
    • Bjorck A., Elfving T., Strakos Z. Stability of Conjugate Gradient and Lanczos methods for linear least squares problems. SIAM J. Matrix Anal. Appl. 19:(3):1998;720-736.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.19 , Issue.3 , pp. 720-736
    • Bjorck, A.1    Elfving, T.2    Strakos, Z.3
  • 2
    • 0000924088 scopus 로고    scopus 로고
    • Estimation of the L-curve via Lanczos bidiagonalization
    • Calvetti D., Golub G.H., Reichel L. Estimation of the L-curve via Lanczos bidiagonalization. BIT. 39:1999;603-619.
    • (1999) BIT , vol.39 , pp. 603-619
    • Calvetti, D.1    Golub, G.H.2    Reichel, L.3
  • 7
    • 0003791218 scopus 로고
    • Conjugate gradient type methods for Ill-posed problems
    • Boca Raton, FL: CRC Press
    • Hanke M., Conjugate Gradient Type Methods for Ill-Posed Problems. Research Notes in Mathematics Series. 1995;CRC Press, Boca Raton, FL.
    • (1995) Research Notes in Mathematics Series
    • Hanke, M.1
  • 8
    • 13344267706 scopus 로고
    • Regularization tools: A MATLAB package for analysis and solution of discrete ill-posed problems
    • Hansen P.C., Regularization Tools: A MATLAB package for analysis and solution of discrete ill-posed problems. Numer. Algorithms. 6:1994;1-35.
    • (1994) Numer. Algorithms , vol.6 , pp. 1-35
    • Hansen, P.C.1
  • 9
    • 0000173054 scopus 로고
    • Test matrices for regularization methods
    • Hansen P.C., Test matrices for regularization methods. SIAM J. Sci. Comput. 16:1995;506-512.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 506-512
    • Hansen, P.C.1
  • 10
    • 0003235718 scopus 로고    scopus 로고
    • Rank-deficient and discrete Ill-posed problems
    • Philadelphia, PA
    • Hansen P.C., Rank-Deficient and Discrete Ill-posed Problems. 1998;SIAM, Philadelphia, PA.
    • (1998) SIAM
    • Hansen, P.C.1
  • 11
    • 0001632418 scopus 로고
    • The use of the L-curve in the regularization of discrete ill-posed problems
    • Hansen P.C., O'Leary D. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. 14:(6):1993;1487-1503.
    • (1993) SIAM J. Sci. Comput. , vol.14 , Issue.6 , pp. 1487-1503
    • Hansen, P.C.1    O'Leary, D.2
  • 12
    • 0030171318 scopus 로고    scopus 로고
    • PET regularization by envelope guided conjugate gradients
    • Kaufman L., Neumaier A. PET regularization by envelope guided conjugate gradients. IEEE Trans. Med. Imag. 15:1996.
    • (1996) IEEE Trans. Med. Imag. , vol.15
    • Kaufman, L.1    Neumaier, A.2
  • 13
    • 84876177882 scopus 로고
    • Solving least squares problems
    • Englewood Cliffs, NJ: Prentice-Hall Philadelphia, PA, 1995
    • Lawson C.L., Hanson R.J. Solving Least Squares Problems. 1974;Prentice-Hall, Englewood Cliffs, NJ. reprinted by SIAM, Philadelphia, PA, 1995.
    • (1974) SIAM
    • Lawson, C.L.1    Hanson, R.J.2
  • 14
    • 0002902522 scopus 로고
    • Least squares methods for ill-posed problems with a prescribed bound
    • Miller K., Least squares methods for ill-posed problems with a prescribed bound. SIAM J. Math. Anal. 1:1970;52-74.
    • (1970) SIAM J. Math. Anal. , vol.1 , pp. 52-74
    • Miller, K.1
  • 16
    • 0001986193 scopus 로고
    • The regularization properties of the adjoint gradient method in ill-posed problems
    • Nemirovskii A.S., The regularization properties of the adjoint gradient method in ill-posed problems. USSR Comput. Math. Phys. 26:(2):1986;332-347.
    • (1986) USSR Comput. Math. Phys. , vol.26 , Issue.2 , pp. 332-347
    • Nemirovskii, A.S.1
  • 17
    • 0001300994 scopus 로고
    • Solution of incorrectly formulated problems and the regularization method
    • English translation of Dokl. Akad. Nauk SSSR 151 (1963) 501-504
    • Tikhonov A.N., Solution of incorrectly formulated problems and the regularization method. Soviet Math. Dokl. 4:1963;1035-1038. English translation of Dokl. Akad. Nauk SSSR 151 (1963) 501-504.
    • (1963) Soviet Math. Dokl. , vol.4 , pp. 1035-1038
    • Tikhonov, A.N.1
  • 18
    • 0001403122 scopus 로고
    • The rate of convergence of conjugate gradients
    • Van der Sluis A., Van der Vorst H.A. The rate of convergence of conjugate gradients. Numer. Math. 48:1986;543-560.
    • (1986) Numer. Math. , vol.48 , pp. 543-560
    • Van der Sluis, A.1    Van der Vorst, H.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.