On convergence rates for the iteratively regularized Gauss-Newton method

IMA Journal of Numerical Analysis

Volumn 17, Issue 3, 1997, Pages 421-436

  Blaschke, Barbara ^a   Neubauer, Andreas ^a   Scherzer, Otmar ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL OPERATORS;

CONVERGENCE RATES; EXACT SOLUTION; ITERATIVELY REGULARIZED GAUSS-NEWTON METHODS; LINEAR ILL-POSED PROBLEMS; NONLINEAR ILL-POSED PROBLEMS; NONLINEAR OPERATOR; SMOOTHNESS CONDITIONS; STOPPING RULE;

NEWTON-RAPHSON METHOD;

EID: 0031532935     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/17.3.421     Document Type: Article

References (11)

1. BAKUSHINSKII, A. B. 1992 The problem of the convergence of the iteratively regularized Gauss-Newton method. Comput. Math. Math. Phys. 32, 1353-9.
2. BAKUSHINSKII, A. B. 1994 private communication.
3. BAKUSHINSKII, A., & GONCHARSKY, A. 1989 Iterative Methods for the Solution of Incorrect Problems. Moscow: Nauka (in Russian).
4. ENGL, H. W., KUNISCH, K., & NEUBAUER, A. 1989 Convergence rates for Tikhonov regularization of nonlinear ill-posed problems. Inverse Problems 5, 523-40.
5. GROETSCH, C. W. 1984 The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind. Boston: Pitman.
6. HANKE, M., NEUBAUER, A., & SCHERZER, O. 1995 A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Numer. Math. 72, 21-37.
7. LOUIS, A. K. 1989 Inverse und schlecht gestellte Probleme. Stuttgart: Teubner.
8. NEUBAUER, A. 1989 Tikhonov regularization for nonlinear ill-posed problems: optimal convergence and finite-dimensional approximation. Inverse Problems 5, 541-57.
9. SCHERZER, O., ENGL, H. W., & KUNISCH, K. 1993 Optimal a-posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problems. SIAM J. Numer. Anal. 30, 1796-838.
10. SEIDMAN, T. I., & VOGEL, C. R. 1989 Well-posedness and convergence of some regularization methods for nonlinear ill-posed problems. Inverse Problems 5, 227-38.
11. VAINIKKO, G. M., & VERETENNIKOV, A. Y. 1986 Iteration Procedures in Ill-Posed Problems. Moscow: Nauka (in Russian).