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Volumn 17, Issue 4, 1996, Pages 956-972

A general heuristic for choosing the regularization parameter in ill-posed problems

Author keywords

A posteriori parameter choice; Conjugate gradients; Ill posed problems; Iterative regularization; Tikhonov regularization

Indexed keywords


EID: 0042208667     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/0917062     Document Type: Article
Times cited : (109)

References (22)
  • 1
    • 0013178793 scopus 로고
    • Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion
    • A. B. BAKUSHINSKII, Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion, USSR Comput. Math, and Math. Phys., 24, 4 (1984), pp. 181-182.
    • (1984) USSR Comput. Math, and Math. Phys. , vol.24 , Issue.4 , pp. 181-182
    • Bakushinskii, A.B.1
  • 2
    • 0041051605 scopus 로고
    • On ill-posed problems and the method of conjugate gradients
    • H. W. Engl and C. W. Groetsch, eds., Academic Press, Boston
    • H. BRAKHAGE, On ill-posed problems and the method of conjugate gradients, in Inverse and Ill-Posed Problems, H. W. Engl and C. W. Groetsch, eds., Academic Press, Boston, 1987, pp. 165-175.
    • (1987) Inverse and Ill-Posed Problems , pp. 165-175
    • Brakhage, H.1
  • 3
    • 0001840812 scopus 로고
    • Regularization methods for the stable solution of inverse problems
    • H. W. ENGL, Regularization methods for the stable solution of inverse problems, Surveys Math. Indust., 3 (1993), pp. 71-143.
    • (1993) Surveys Math. Indust. , vol.3 , pp. 71-143
    • Engl, H.W.1
  • 4
    • 0000797172 scopus 로고
    • A posteriori parameter choice for generalized regularization methods for solving linear ill-posed problems
    • H. W. ENGL AND H. GFRERER, A posteriori parameter choice for generalized regularization methods for solving linear ill-posed problems, Appl. Numer. Math., 4 (1988), pp. 395-417.
    • (1988) Appl. Numer. Math. , vol.4 , pp. 395-417
    • Engl, H.W.1    Gfrerer, H.2
  • 5
    • 84966214028 scopus 로고
    • An a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates
    • H. GFRERER, An a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates. Math. Comp., 49 (1987), pp. 507-522.
    • (1987) Math. Comp. , vol.49 , pp. 507-522
    • Gfrerer, H.1
  • 7
    • 0038618747 scopus 로고
    • Accelerated Landweber iterations for the solution of ill-posed equations
    • M. HANKE, Accelerated Landweber iterations for the solution of ill-posed equations, Numer. Math.. 60 (1991), pp. 341-373.
    • (1991) Numer. Math. , vol.60 , pp. 341-373
    • Hanke, M.1
  • 8
    • 0027642363 scopus 로고
    • An ε-free a posteriori stopping rule for certain iterative regularization methods
    • _, An ε-free a posteriori stopping rule for certain iterative regularization methods, SIAM J. Numer. Anal., 30 (1993), pp. 1208-1228.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1208-1228
  • 9
    • 0003236641 scopus 로고
    • Conjugate Gradient Type Methods for Ill-Posed Problems
    • Longman, Harlow
    • _, Conjugate Gradient Type Methods for Ill-Posed Problems, Pitman Res. Notes Math., Longman, Harlow, 1995.
    • (1995) Pitman Res. Notes Math.
  • 10
    • 0343303330 scopus 로고
    • An optimal stopping rule for the ν-method for solving ill-posed problems, using Christoffel functions
    • M. HANKE AND H. W. ENGL, An optimal stopping rule for the ν-method for solving ill-posed problems, using Christoffel functions, J. Approx. Theory, 79 (1994), pp. 89-108.
    • (1994) J. Approx. Theory , vol.79 , pp. 89-108
    • Hanke, M.1    Engl, H.W.2
  • 11
    • 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
  • 12
    • 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 Review, 34 (1992), pp. 561-580.
    • (1992) SIAM Review , vol.34 , pp. 561-580
    • Hansen, P.C.1
  • 13
    • 0008347326 scopus 로고
    • On the choice of regularization parameters by means of the quasi-optimality and ratio criteria
    • A. S. LEONOV, On the choice of regularization parameters by means of the quasi-optimality and ratio criteria, Soviet Math. Dokl., 19 (1978), pp. 537-540.
    • (1978) Soviet Math. Dokl. , vol.19 , pp. 537-540
    • Leonov, A.S.1
  • 15
    • 38249043048 scopus 로고
    • The regularization properties of the adjoint gradient method in ill-posed problems
    • A. S. NEMIROVSKII, The regularization properties of the adjoint gradient method in ill-posed problems, USSR Comput. Math. and Math. Phys., 26, 2 (1986), pp. 7-16.
    • (1986) USSR Comput. Math. and Math. Phys. , vol.26 , Issue.2 , pp. 7-16
    • Nemirovskii, A.S.1
  • 16
    • 85033018971 scopus 로고    scopus 로고
    • On converse and saturation results for Tikhonov regularization of linear ill-posed problems
    • to appear
    • A. NEUBAUER, On converse and saturation results for Tikhonov regularization of linear ill-posed problems, SIAM J. Numer. Anal., to appear.
    • SIAM J. Numer. Anal.
    • Neubauer, A.1
  • 17
    • 0002729317 scopus 로고
    • The principle of the residual in the solution of ill-posed problems with nonselfadjoint operator
    • In Russian
    • T. RAUS, The principle of the residual in the solution of ill-posed problems with nonselfadjoint operator, Uchen. Zap. Tartu Gos. Univ., 715 (1985), pp. 12-20. (In Russian.)
    • (1985) Uchen. Zap. Tartu Gos. Univ. , vol.715 , pp. 12-20
    • Raus, T.1
  • 18
    • 0008442191 scopus 로고
    • Use of the regularization method in non-linear problems
    • A.N. TIKHONOV AND V. B. GLASKO, Use of the regularization method in non-linear problems, USSR Comput. Math, and Math. Phys., 5, 3 (1965), pp. 93-107.
    • (1965) USSR Comput. Math, and Math. Phys. , vol.5 , Issue.3 , pp. 93-107
    • Tikhonov, A.N.1    Glasko, V.B.2
  • 19
    • 0039599972 scopus 로고
    • Error estimates of the successive approximation method for ill-posed problems
    • G. M. VAINIKKO, Error estimates of the successive approximation method for ill-posed problems, Automat. Remote Control, 40 (1980), pp. 356-363.
    • (1980) Automat. Remote Control , vol.40 , pp. 356-363
    • Vainikko, G.M.1
  • 21
    • 85033739150 scopus 로고    scopus 로고
    • Non-convergence of the L-curve regularization parameter selection method
    • to appear
    • C. VOGEL, Non-convergence of the L-curve regularization parameter selection method, Inverse Problems, to appear.
    • Inverse Problems
    • Vogel, C.1
  • 22
    • 0003466536 scopus 로고
    • Society for Industrial and Applied Mathematics, Philadelphia
    • G. WAHBA, Spline Models for Observational Data, Society for Industrial and Applied Mathematics, Philadelphia, 1990.
    • (1990) Spline Models for Observational Data
    • Wahba, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.