Parameter identification by regularization for surface representation via the moving grid approach

SIAM Journal on Control and Optimization

Volumn 42, Issue 4, 2003, Pages 1416-1430

  Kindermann, Stefan ^a   Neubauer, Andreas ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Ill posed problems; Parameter identification; Regularization via moving grids

Indexed keywords

DIFFUSION PARAMETERS; ILL-POISED EQUATIONS; ILL-POISED PROBLEMS; LEAST SQUARE SOLUTIONS;

ALGORITHMS; FUNCTIONS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PROBLEM SOLVING; RUNGE KUTTA METHODS;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 4043181913     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902408034     Document Type: Article

References (20)

1. B. BLASCHKE, A. NEUBAUER, AND O. SCHERZER, On convergence rates for the iteratively regularized Gauss-Newton method, IMA J. Numer. Anal., 17 (1997), pp. 421-436.
2. P. BOCHEV, G. LIAO, AND G. DELA PENA, Analysis and computation for adaptive moving grids by deformation, Numer. Methods Partial Differential Equations, 12 (1996), pp. 489-506.
3. M. BURGER AND W. MÜHLHUBER, Iterative regularization of parameter identification problems by sequential quadratic programming methods, Inverse Problems, 18 (2002), pp. 943-969.
4. Z. CHEN AND J. ZOU, An augmented Lagrangian method for identifying discontinuous parameters in elliptic systems, SIAM J. Control. Optim, 37 (1999), pp. 892-910.
5. H. W. ENGL, M. HANKE, AND A. NEUBAUER, Regularization of Inverse Problems, Kluwer, Dordrecht, The Netherlands, 1996.
6. K. ITO, M. KROLLER, AND K. KUNISCH, A numerical study of an augmented Lagrangian method for the estimation of parameters in elliptic systems, SIAM J. Sci. Statist. Comput., 12 (1991), pp. 884-910.
7. K. ITO AND K. KUNISCH, On the injectivity and linearization of the coefficient-to-solution mapping for elliptic boundary value problems, J. Math. Anal. Appl., 188 (1994), pp. 1040-1066.
8. S. KINDERMANN, Regularization of Ill-Posed Problems with Discontinuous Solutions by Curve and Surface Representations, Ph.D. thesis, University of Linz, Austria, 2001.
9. 1-Curve, Technical report 1/1999, Industrial Mathematics Institute, University of Linz, Austria, 1999.
10. S. KINDERMANN AND A. NEUBAUER, Identification of discontinuous parameters by regularization for curve representations, Inverse Problems, 15 (1999), pp. 1559-1572.
11. S. KINDERMANN AND A. NEUBAUER, Estimation of discontinuous parameters of elliptic partial differential equations by regularization for surface representations, Inverse Problems, 17 (2001), pp. 789-803.
12. S. KINDERMANN AND A. NEUBAUER, Regularization for surface representations of discontinuous solutions of linear ill-posed problems, Numer. Funct. Anal. Optim., 22 (2001), pp. 79-105.
13. R. LUCE AND S. PEREZ, Parameter identification for an elliptic partial differential equation with distributed noisy data, Inverse Problems, 15 (1999), pp. 291-307.
14. A. NEUBAUER, Estimation of discontinuous solutions of ill-posed problems by regularization for surface representations: Numerical realization via moving grids, in Recent Developments in Theories and Numerics, International Conference on Inverse Problems, Y. C. Hon, M. Yamamoto, J. Cheng, and J. Y. Lee, eds., World Scientific, Singapore, 2003, pp. 67-83.
15. A. NEUBAUER AND O. SCHERZER, A convergent rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems, Z. Anal. Anwendungen, 14 (1995), pp. 369-377.
16. A. NEUBAUER AND O. SCHERZER, Reconstruction of discontinuous solutions from blurred data, in Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications, Proc. SPIE 3171, R. L. Barbour, M. J. Carvlin, and M. A. Fiddy, eds., SPIE, Bellingham, WA, 1997, pp. 34-41.
17. A. NEUBAUER AND O. SCHERZER, Regularization for curve representations: Uniform convergence for discontinuous solutions of ill-posed problems, SIAM J. Appl. Math., 58 (1998), pp. 1891-1900.
18. G. R. RICHTER, An inverse problem for the steady state diffusion equation, SIAM J. Appl. Math., 41 (1981), pp. 210-221.
19. W. RING, Structural properties of solutions of total variation regularization problems, M2AN Math. Model. Numer. Anal., 34 (2000), pp. 799-810.
20. B. SEMPER AND G. LIAO, A moving grid finite element method using grid deformation, Numer. Methods Partial Differential Equations, 11 (1995), pp. 603-615.