메뉴 건너뛰기




Volumn 44, Issue 1, 2006, Pages 153-182

Regularizing Newton-kaczmarz methods for nonlinear ill-posed problems

Author keywords

Ill posed problems; Newton Kaczmarz methods; Tomography

Indexed keywords

ITERATIVE METHODS; MATHEMATICAL MODELS; PROBLEM SOLVING; THEOREM PROVING;

EID: 33847617979     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040613779     Document Type: Article
Times cited : (59)

References (34)
  • 1
    • 0000834834 scopus 로고
    • The problem of the convergence of the iteratively regularized Gauss-Newton method
    • A. B. BAKUSHINSKII, The problem of the convergence of the iteratively regularized Gauss-Newton method, Comput. Math. Math. Phys., 32 (1992), pp. 1353-1359.
    • (1992) Comput. Math. Math. Phys , vol.32 , pp. 1353-1359
    • BAKUSHINSKII, A.B.1
  • 2
    • 33847619410 scopus 로고    scopus 로고
    • A. B. BAKUSHINSKII AND M. YU. KOKURIN, Iterative Methods for Approximate Solution of Inverse Problems, Springer, Dordrecht, The Netherlands, 2004.
    • A. B. BAKUSHINSKII AND M. YU. KOKURIN, Iterative Methods for Approximate Solution of Inverse Problems, Springer, Dordrecht, The Netherlands, 2004.
  • 4
    • 0036683969 scopus 로고    scopus 로고
    • Iterative regularization of parameter identification problems by SQP methods
    • M. BURGER AND W. MÜHLHUBER, Iterative regularization of parameter identification problems by SQP methods, Inverse Problems, 18 (2002), pp. 943-970.
    • (2002) Inverse Problems , vol.18 , pp. 943-970
    • BURGER, M.1    MÜHLHUBER, W.2
  • 5
    • 0010048713 scopus 로고    scopus 로고
    • Numerical approximation of an SQP-type method for parameter identification
    • M. BURGER AND W. MÜHLHUBER, Numerical approximation of an SQP-type method for parameter identification, SIAM J. Numer. Anal., 40 (2002), pp. 1775-1797.
    • (2002) SIAM J. Numer. Anal , vol.40 , pp. 1775-1797
    • BURGER, M.1    MÜHLHUBER, W.2
  • 6
    • 0345875999 scopus 로고    scopus 로고
    • A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions
    • P. DEUPLHARD, H. W. ENGL, AND O. SCHERZER, A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions, Inverse Problems, 14 (1998), pp. 1081-1106.
    • (1998) Inverse Problems , vol.14 , pp. 1081-1106
    • DEUPLHARD, P.1    ENGL, H.W.2    SCHERZER, O.3
  • 7
    • 0001820687 scopus 로고
    • Affine invariant convergence theorems for Newton's method and extensions to related methods
    • P. DEUFLHARD AND G. HEINDL, Affine invariant convergence theorems for Newton's method and extensions to related methods, SIAM J. Numer. Anal., 16 (1979), pp. 1-10.
    • (1979) SIAM J. Numer. Anal , vol.16 , pp. 1-10
    • DEUFLHARD, P.1    HEINDL, G.2
  • 9
    • 0000574920 scopus 로고    scopus 로고
    • A nonlinear inversion method for 3D-electromagnetic imaging using adjoint fields
    • O. DORN, H. BERTETE-AGUIRRE, J. G. BERRYMAN, AND G. C. PAPANICOLAOU, A nonlinear inversion method for 3D-electromagnetic imaging using adjoint fields, Inverse Problems, 15 (1999), pp. 1523-1558.
    • (1999) Inverse Problems , vol.15 , pp. 1523-1558
    • DORN, O.1    BERTETE-AGUIRRE, H.2    BERRYMAN, J.G.3    PAPANICOLAOU, G.C.4
  • 12
    • 0028484827 scopus 로고
    • Reconstruction of semiconductor doping profile from LBIC image
    • W. FANG AND K. ITO, Reconstruction of semiconductor doping profile from LBIC image, SIAM J. Appl. Math., 54 (1994), pp. 1067-1082.
    • (1994) SIAM J. Appl. Math , vol.54 , pp. 1067-1082
    • FANG, W.1    ITO, K.2
  • 14
    • 0031275314 scopus 로고    scopus 로고
    • Regularizing properties of a truncated Newton-CG algorithm for nonlinear inverse problems
    • M. HANKE, Regularizing properties of a truncated Newton-CG algorithm for nonlinear inverse problems, Numer. Funct. Anal. Optim., 18 (1997), pp. 971-993.
    • (1997) Numer. Funct. Anal. Optim , vol.18 , pp. 971-993
    • HANKE, M.1
  • 15
    • 0003062572 scopus 로고    scopus 로고
    • A regularization Levenberg-Marquardt scheme, with applications to inverse ground-water filtration problems
    • M. HANKE, A regularization Levenberg-Marquardt scheme, with applications to inverse ground-water filtration problems, Inverse Problems, 13 (1997), pp. 79-95.
    • (1997) Inverse Problems , vol.13 , pp. 79-95
    • HANKE, M.1
  • 16
  • 17
    • 0040893030 scopus 로고
    • A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
    • M. HANKE, A. NEUBAUER, AND O. SCHERZER, A convergence analysis of the Landweber iteration for nonlinear ill-posed problems, Numer. Math., 72 (1995), pp. 21-37.
    • (1995) Numer. Math , vol.72 , pp. 21-37
    • HANKE, M.1    NEUBAUER, A.2    SCHERZER, O.3
  • 18
    • 0001421314 scopus 로고
    • Influence factors of ill-posedness for nonlinear ill-posed problems
    • B. HOFMANN AND O. SCHERZER, Influence factors of ill-posedness for nonlinear ill-posed problems, Inverse Problems, 10 (1994), pp. 1277-1297.
    • (1994) Inverse Problems , vol.10 , pp. 1277-1297
    • HOFMANN, B.1    SCHERZER, O.2
  • 20
    • 0034187252 scopus 로고    scopus 로고
    • Regularization of exponentially ill-posed problems
    • T. HOHAGE, Regularization of exponentially ill-posed problems, Numer. Funct. Anal. Optim., 21 (2000), pp. 439-464.
    • (2000) Numer. Funct. Anal. Optim , vol.21 , pp. 439-464
    • HOHAGE, T.1
  • 21
    • 85120508024 scopus 로고    scopus 로고
    • B. BLASCHKE(-KALTENBACHER), A. NEUBAUER, AND O. SCHERZER, On convergence rates for the iteratively regularized Gauss-Newton method, IMA J. Numer. Anal., 17 (1997), pp. 421-436.
    • B. BLASCHKE(-KALTENBACHER), A. NEUBAUER, AND O. SCHERZER, On convergence rates for the iteratively regularized Gauss-Newton method, IMA J. Numer. Anal., 17 (1997), pp. 421-436.
  • 22
    • 0000130782 scopus 로고    scopus 로고
    • Some Newton type methods for the regularization of nonlinear ill-posed problems
    • B. KALTENBACHER, Some Newton type methods for the regularization of nonlinear ill-posed problems, Inverse Problems, 13 (1997), pp. 729-753.
    • (1997) Inverse Problems , vol.13 , pp. 729-753
    • KALTENBACHER, B.1
  • 24
    • 33744541048 scopus 로고    scopus 로고
    • Convergence analysis of a Landweber-Kaczmarz method for solving nonlinear ill-posed problems
    • S. Romanov, S. I. Kabanikhin, Y. E. Anikonov, A. L. Bukhgein, eds, VSP Publishers, Zeist, The Netherlands
    • R. KOWAR AND O. SCHERZER, Convergence analysis of a Landweber-Kaczmarz method for solving nonlinear ill-posed problems, in Ill-Posed and Inverse Problems, S. Romanov, S. I. Kabanikhin, Y. E. Anikonov, A. L. Bukhgein, eds., VSP Publishers, Zeist, The Netherlands, 2002.
    • (2002) Ill-Posed and Inverse Problems
    • KOWAR, R.1    SCHERZER, O.2
  • 26
    • 0001517321 scopus 로고
    • The determination of multiple coefficients in a second order differential equation from input sources
    • B. LOWE AND W. RUNDELL, The determination of multiple coefficients in a second order differential equation from input sources, Inverse Problems, 9 (1993), pp. 469-482.
    • (1993) Inverse Problems , vol.9 , pp. 469-482
    • LOWE, B.1    RUNDELL, W.2
  • 27
    • 0028320254 scopus 로고
    • The determination of a coefficient in a parabolic equation from input sources
    • B. LOWE AND W. RUNDELL, The determination of a coefficient in a parabolic equation from input sources, IMA J. Appl. Math., 52 (1994), pp. 31-50.
    • (1994) IMA J. Appl. Math , vol.52 , pp. 31-50
    • LOWE, B.1    RUNDELL, W.2
  • 30
    • 0004224347 scopus 로고    scopus 로고
    • Numerical Solution of Bilinear Inverse Problems
    • Technical Report, University of Münster, Germany
    • F. NATTERER, Numerical Solution of Bilinear Inverse Problems, Technical Report, University of Münster, Germany, 1996.
    • (1996)
    • NATTERER, F.1
  • 31
    • 0032642260 scopus 로고    scopus 로고
    • A numerical method for solving nonlinear ill-posed problems
    • A. G. RAMM AND A. B. SMIRNOVA, A numerical method for solving nonlinear ill-posed problems, Nonlinear Funct. Anal. Optim., 20 (1999), pp. 317-332.
    • (1999) Nonlinear Funct. Anal. Optim , vol.20 , pp. 317-332
    • RAMM, A.G.1    SMIRNOVA, A.B.2
  • 32
    • 0035590701 scopus 로고    scopus 로고
    • On convergence rates of inexact Newton regularizations
    • A. RIEDER, On convergence rates of inexact Newton regularizations, Numer. Math., 88 (2001), pp. 347-365.
    • (2001) Numer. Math , vol.88 , pp. 347-365
    • RIEDER, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.