메뉴 건너뛰기




Volumn 38, Issue 1, 1998, Pages 45-68

A modified Landweber iteration for solving parameter estimation problems

Author keywords

Modified Landweber iteration; Nonlinear ill posed problems; Regularization methods; Stopping rules

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PARAMETER ESTIMATION; PROBLEM SOLVING;

EID: 0032122772     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900081     Document Type: Article
Times cited : (70)

References (17)
  • 1
    • 0000834834 scopus 로고
    • The problem of the iteratively regularized Gauss-Newton method
    • Bakushinskii AB (1992) The problem of the iteratively regularized Gauss-Newton method. Comput Math Math Phys 32:1353-1359
    • (1992) Comput Math Math Phys , vol.32 , pp. 1353-1359
    • Bakushinskii, A.B.1
  • 2
    • 0345413728 scopus 로고
    • Iterative methods for solving non-linear operator equations without condition of regularity
    • in Russian
    • Bakushinskii AB (1993) Iterative methods for solving non-linear operator equations without condition of regularity. Soviet Math Dokl 330:282-284 (in Russian)
    • (1993) Soviet Math Dokl , vol.330 , pp. 282-284
    • Bakushinskii, A.B.1
  • 4
    • 0004870127 scopus 로고    scopus 로고
    • On the Landweber iteration for nonlinear ill-posed problems
    • Binder A, Hanke M, Scherzer O (1996) On the Landweber iteration for nonlinear ill-posed problems. J Inverse Ill-Posed Problems 4:381-389
    • (1996) J Inverse Ill-Posed Problems , vol.4 , pp. 381-389
    • Binder, A.1    Hanke, M.2    Scherzer, O.3
  • 5
    • 0031532935 scopus 로고    scopus 로고
    • On convergence rates for the iteratively regularized Gauss-Newton method
    • Blaschke B, Neubauer A, Scherzer O (1997) On convergence rates for the iteratively regularized Gauss-Newton method. IMA J Numer Anal 17:429-436
    • (1997) IMA J Numer Anal , vol.17 , pp. 429-436
    • Blaschke, B.1    Neubauer, A.2    Scherzer, O.3
  • 6
    • 0030127690 scopus 로고    scopus 로고
    • On weakly nonlinear inverse problems
    • Chavent G. Kunisch K (1996) On weakly nonlinear inverse problems. SIAM J Appl Math 56:542-572
    • (1996) SIAM J Appl Math , vol.56 , pp. 542-572
    • Chavent, G.1    Kunisch, K.2
  • 7
    • 36149030945 scopus 로고
    • Convergence rates for Tikhonov regularization of nonlinear ill-posed problems
    • Engl HW, Kunisch K, Neubauer A (1989) Convergence rates for Tikhonov regularization of nonlinear ill-posed problems. Inverse Problems 5:523-540
    • (1989) Inverse Problems , vol.5 , pp. 523-540
    • Engl, H.W.1    Kunisch, K.2    Neubauer, A.3
  • 8
    • 0040893030 scopus 로고
    • A convergence analysis of Landweber iteration for nonlinear ill-posed problems
    • Hanke M, Neubauer A, Scherzer O (1995) A convergence analysis of Landweber iteration for nonlinear ill-posed problems. Numer Math 72:21-35
    • (1995) Numer Math , vol.72 , pp. 21-35
    • Hanke, M.1    Neubauer, A.2    Scherzer, O.3
  • 9
    • 0001421314 scopus 로고
    • Factors influencing the ill-posedness of nonlinear ill-posed problems
    • Hofmann B, Scherzer O (1994) Factors influencing the ill-posedness of nonlinear ill-posed problems. Inverse Problems 10:1277-1297
    • (1994) Inverse Problems , vol.10 , pp. 1277-1297
    • Hofmann, B.1    Scherzer, O.2
  • 10
    • 0016470075 scopus 로고
    • A uniform approach to gradient methods for linear operator equations
    • McCormick SF, Rodrigue GH (1975) A uniform approach to gradient methods for linear operator equations. J Math Anal Appl 49:275-285
    • (1975) J Math Anal Appl , vol.49 , pp. 275-285
    • McCormick, S.F.1    Rodrigue, G.H.2
  • 11
    • 84966213836 scopus 로고
    • When do Sobolev spaces form a Hubert scale?
    • Neubauer A (1988) When do Sobolev spaces form a Hubert scale? Proc Amer Math Soc 103:557-562
    • (1988) Proc Amer Math Soc , vol.103 , pp. 557-562
    • Neubauer, A.1
  • 12
    • 0001425652 scopus 로고
    • Tikhonov regularization for non-linear ill-posed problems: Optimal convergence rates and finite-dimensional approximation
    • Neubauer A (1989) Tikhonov regularization for non-linear ill-posed problems: optimal convergence rates and finite-dimensional approximation. Inverse Problems 5:541-557
    • (1989) Inverse Problems , vol.5 , pp. 541-557
    • Neubauer, A.1
  • 13
    • 84972955608 scopus 로고
    • Finite-dimensional approximation of Tikhonov regularized solutions of non-linear ill-posed problems
    • Neubauer A, Scherzer O (1990) Finite-dimensional approximation of Tikhonov regularized solutions of non-linear ill-posed problems. Numer Funct Anal Optim 11:85-99
    • (1990) Numer Funct Anal Optim , vol.11 , pp. 85-99
    • Neubauer, A.1    Scherzer, O.2
  • 14
    • 0010014032 scopus 로고
    • Convergence criteria of iterative methods based on Landweber iteration for nonlinear problems
    • Scherzer O (1995) Convergence criteria of iterative methods based on Landweber iteration for nonlinear problems. J Math Anal Appl 194:911-933
    • (1995) J Math Anal Appl , vol.194 , pp. 911-933
    • Scherzer, O.1
  • 15
    • 0041098562 scopus 로고    scopus 로고
    • A convergence analysis of a method of steepest descent and a two-step algorithm for nonlinear ill-posed problems
    • Scherzer O (1996) A convergence analysis of a method of steepest descent and a two-step algorithm for nonlinear ill-posed problems. Numer Funct Anal Optim 17:197-214
    • (1996) Numer Funct Anal Optim , vol.17 , pp. 197-214
    • Scherzer, O.1
  • 16
    • 0027802743 scopus 로고
    • Optimal a posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problems
    • Scherzer O, Engl HW, Kunisch K (1993) Optimal a posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problems. SIAM J Numer Anal 30:1796-1838
    • (1993) SIAM J Numer Anal , vol.30 , pp. 1796-1838
    • Scherzer, O.1    Engl, H.W.2    Kunisch, K.3
  • 17
    • 0000027929 scopus 로고
    • Well posedness and convergence of some regularisation methods for non-linear ill-posed problems
    • Seidman TI, Vogel CR (1989) Well posedness and convergence of some regularisation methods for non-linear ill-posed problems. Inverse Problems 10:227-238
    • (1989) Inverse Problems , vol.10 , pp. 227-238
    • Seidman, T.I.1    Vogel, C.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.