Iterative methods for the reconstruction of an inverse potential problem

Inverse Problems

Volumn 12, Issue 3, 1996, Pages 251-266

  Hettlich, Frank ^a   Rundell, William ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000298487     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/12/3/006     Document Type: Article

References (15)

1. Bakkushinskii A B 1992 The problem of the iteratively reglularized Gauss-Newton method Comput. Maths. Math. Phys. 21 1353-1399
2. Binder A. Hanke M and Scherzer O 1996 On the Landweber iteration for nonlinear ill-posed problems J. Inverse and Ill-posed Problems to appear
3. Cabayan H S and Belford G G 1971 On computing a stable least squares solution to the inverse problem for a planar Newtonian potential, SIAM J. Appl. Math. 20 51-61
4. Colton D L and Kress R 1983 Integral Equation Methods in Scattering Theory (New York: Wiley Interscience)
5. 1990 Handbook of Numerical Analysis vol 1, ed P G Ciarlet and J L Lions (Amsterdam: North-Holland)
6. Gilbarg D and Trudinger N S 1983 Elliptic Partial Differential Equations of Second Order (Berlin: Springer)
7. Hanke M, Hettlich F and Scherzer O 1995 The Landweber iteration for an inverse scattering problem Proc. 1995 Design Engineering Technical Conf. vol 3, Part C Vibration Control, Analysis, and Identification ed K-W Wang et al (New York: The American Society of Mechanical Engineers) pp 909-15
8. Hanke M, Neubauer A and Scherzer O 1995 A convergence analysis of the Landweber iteration fro nonlinear ill-posed problems Numer. Math. 72 21-37
9. Hettlich F 1995 Fréchet derivatives in inverse obstacle scattering Inverse Problems 11 371-382
10. Isakov V 1990 Inverse source problems Mathematical Surveys and Monographs vol 34 (Providence, RI: American mathematical Society)
11. Kirsch A 1993 The domain derivative and two applications in inverse scattering theory Inverse Problems 9 81-96
12. Kunisch K and Pan X 1994 Estimation of interfaces from boundary measurements. SIAM J. Control Optm. 32 1643-1674
13. Ring W 1995 Identification of a core form boundary data, SIAM J. Appl. Math 55 677-706
14. Scherzer O 1996 A regularized Landweber iteration for solving parameter estimation problems, submitted
15. Sokolowski J and Zolesio J-P 1992 Introduction to Shape Optimization (Berlin: Springer)