A computational method for the inverse transmission eigenvalue problem

Inverse Problems

Volumn 29, Issue 10, 2013, Pages

  Gintides, Drossos ^a   Pallikarakis, Nikolaos ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

A-PROPER OPERATORS; ANALYTIC COMPUTATIONS; NEWTON-TYPE ALGORITHMS; PIECE-WISE CONSTANTS; QUADRATIC EIGENVALUE PROBLEMS; TRANSMISSION EIGENVALUE; TRANSMISSION EIGENVALUES; TRANSMISSION PROBLEM;

ALGORITHMS; COMPUTATIONAL METHODS; GALERKIN METHODS; INVERSE PROBLEMS; REFRACTIVE INDEX;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 84884649591     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/29/10/104010     Document Type: Article

References (34)

1. Aktosun T, Gintides D and Papanikolaou V G 2011 The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation Inverse Problems 27 115004
2. Babuška I and Osborn J 1991 Eigenvalue problems Handbook of Numerical Analysis vol 2 (Amsterdam: Elsevier) pp 641-787
3. Cakoni F, Cayoren M and Colton D 2008 Transmission eigenvalues and the nondestructive testing of dielectrics Inverse Problems 24 065016
4. Cakoni F, Colton D and Haddar H 2009 The computation of lower bounds for the norm of the index of refraction in an anisotropic media J. Integral Eqns Appl. 21 203-27
5. Cakoni F, Colton D and Haddar H 2010 On the determination of Dirichlet and transmission eigenvalues from far field data C. R. Math. 348 379-83
6. Cakoni F, Colton D and Monk P 2007 On the use of transmission eigenvalues to estimate the index of refraction from far field data Inverse Problems 23 507-22 (Pubitemid 46453820)
7. Cakoni F, Colton D and Gintides D 2010 The transmission eigenvalue problem Advanced Topics in Scattering and Biomedical Engineering: Proc. 9th Int. Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering ed A Charalambopoulos, D I Fotiadis and D Polyzos (Singapore: World Scientific) pp 368-80
8. Cakoni F, Colton D and Gintides D 2010 The interior transmission eigenvalue problem SIAM J. Math. Anal. 42 2912-21
9. Cakoni F, Colton D, Monk P and Sun J 2010 The inverse electromagnetic scattering problem for anisotropic media Inverse Problems 26 074004
10. Cakoni F and Gintides D 2010 New results on transmission eigenvalues Inverse Problems Imaging 4 39-48
11. Cakoni F, Gintides D and Haddar H 2010 The existence of an infinite discrete set of transmission eigenvalues SIAM J. Math. Anal. 42 237-55
12. Cakoni F and Haddar H 2012 Transmission eigenvalues in inverse scattering theory Inverse Problems and Applications: Inside Out II (MSRI Publications 60) ed G Uhlmann (Cambridge: Cambridge University Press) pp 527-78
13. Cakoni F and Haddar H 2009 On the existence of transmission eigenvalues in an inhomogeneous medium Appl. Anal. 88 475-93
14. Colton D and Kress R 1998 Inverse Acoustic and Electromagnetic Scattering Theory 2nd edn (Berlin: Springer)
15. Colton D and Monk P 1988 The inverse scattering problem for time-harmonic acoustic waves in an inhomogeneous medium Q. J. Mech. Appl. Math. 41 97-125
16. Colton D, Monk P and Sun J 2010 Analytical and computational methods for transmission eigenvalues Inverse Problems 26 045011
17. Colton D, Päivärinta L and Sylvester J 2007 The interior transmission problem Inverse Problems Imaging 1 13-28
18. Descloux J, Nassif N and Rapaz J 1978 On spectral approximation: part 1. The problem of convergence RAIRO Anal. Numer. 12 97-112
19. Elhay S and Ram Y M 2002 An affine inverse eigenvalue problem Inverse Problems 18 455-66 (Pubitemid 34428530)
20. Gladwell G M L 2004 Inverse Problems in Vibration (Solid Mechanics and Its Applications) 2nd edn (New York: Academic)
21. Gohberg I, Goldberg S and Kaashoek A M 2000 Basic Classes of Linear Operators (Basel: Birkhäuser)
22. Gould S H 1996 Variational Methods for Eigenvalue Problems (New York: Dover)
23. Ji X, Sun J and Turner T 2012 Algorithm 922: a mixed finite element method for Helmholtz transmission eigenvalues ACM Trans. Math. Softw. 38 1-8
24. Kirsch A 2009 On the existence of transmission eigenvalues Inverse Problems Imaging 3 155-72
25. Lancaster P and Tismenetsky M 1985 The Theory of Matrices 2nd edn (London: Academic)
26. Leung Y and Colton D 2012 Complex transmission eigenvalues for spherically stratified media Inverse Problems 28 075005
27. McLaughlin J R and Polyakov P L 1994 On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues J. Differ. Eqns 107 351-82
28. McLaughlin J R, Polyakov P L and Sacks P E 1994 Reconstruction of a spherically symmetric speed of sound SIAM J. Appl. Math. 54 1203-23
29. McLaughlin J R, Sacks P E and Somasundaram M 1997 Inverse scattering in acoustic media using interior transmission eigenvalues Inverse Problems in Wave Propagation ed G Chavent, G Papanicolaou, P Sacks and W Symes (Berlin: Springer) pp 357-74
30. Päivärinta L and Sylvester J 2008 Transmission eigenvalues SIAM J. Math. Anal. 40 738-53
31. Rynne B P and Sleeman B D 1992 The interior transmission problem and inverse scattering from inhomogeneous media SIAM J. Math. Anal. 22 1755-62
32. Sun J 2011 Iterative methods for transmission eigenvalues SIAM J. Numer. Anal. 49 1860-74
33. Sun J 2011 Estimation of transmission eigenvalues and the index of refraction from Cauchy data Inverse Problems 27 015009
34. Tisseur F and Meerbergen K 2001 The quadratic eigenvalue problem SIAM Rev. 43 235-86 (Pubitemid 32697793)