A Newton-type method for a transmission problem in inverse scattering

Inverse Problems

Volumn 14, Issue 5, 1998, Pages 1207-1227

  Hohage, T ^a   Schormann, C ^b  

^a Inst für Industriemathematik   (Austria)

^b Inst F Numerische Angew Math   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000726131     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/14/5/008     Document Type: Article

References (15)

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. Blaschke B, Neubauer A and Scherzer O 1997 On convergence rates for the iteratively regularized Gauss-Newton method IMA J. Numer. Anal. 17 421-36
3. Colton D and Kress R 1983 Integral Equation Methods in Scattering Theory (New York: Wiley)
4. Hettlich F 1995 Fréchet derivatives in inverse obstacle scattering Inverse Problems 11 371-82
5. Hohage T 1996 Newton-Verfahren beim inversen Neumann-Problem zur Helmholtz-Gleichung Diplomarbeit Göttingen
6. Hohage T 1997 Logarithmic convergence rates of the iteratively regularized Gauss-Newton method for an inverse potential and an inverse scattering problem Inverse Problems 13 1279-99
7. Hohage T Convergence rates of a regularized Newton method in sound-hard inverse scattering SIAM J. Numer. Anal. to appear
8. Kleinman R E and Martin P A 1988 On single integral equations for the transmission problem of acoustics SIAM J. Appl. Math. 48 307-25
9. Kress R 1989 Linear Integral Equations (Berlin: Springer)
10. Kress R 1995 On the numerical solution of a hypersingular integral equation in scattering theory J. Comput. Appl. Math. 61 345-60
11. Kress R and Roach G F 1978 Transmission problems for the Helmholtz equation J. Math. Phys. 19 1433-7
12. Kress R and Sloan I H 1993 On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation Numer. Math. 66 199-214
13. Potthast R 1994 Fréchet differentiability of boundary integral operators in inverse scattering Inverse Problems 10 431-47
14. Schormann C 1996 Newton-Verfahren für ein inverses Transmissionsproblem bei elektromagnetischen Wellen Diplomarbeit Göttingen
15. Tautenhahn U 1996 Optimality for linear ill-posed problems under general source conditions Preprint IP 5 University Chemitz-Zittau