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On rational approximation methods for inverse source problems
1. | Institute of Mathematics, Johannes Gutenberg-Universität, 55099 Mainz |
2. | Department of Mathematics, Texas A&M University, College Station, TX 77843-3368 |
References:
[1] |
L. V. Ahlfors, "Complex Analysis," McGraw-Hill, New York, third edition, 1979. |
[2] |
S. Andrieux and A. Ben Abda, Identification of planar cracks by complete overdetermined data: inversion formulae, Inverse Problems, 12 (1996), 553-563.
doi: 10.1088/0266-5611/12/5/002. |
[3] |
G. A. Baker and P. Graves-Morris, "Padé Approximants," Cambridge University Press, Cambridge, second edition, 1996. |
[4] |
L. Baratchart, A. Ben Abda, F. Ben Hassen and J. Leblond, Recovery of pointwise sources or small inclusions in 2D domains and rational approximation, Inverse Problems, 21 (2005), 51-74.
doi: 10.1088/0266-5611/21/1/005. |
[5] |
L. Baratchart, J. Leblond, F. Mandréa and E. B. Saff, How can the meromorphic approximation help to solve some 2D inverse problems for the Laplacian? Inverse Problems, 15 (1999), 79-90.
doi: 10.1088/0266-5611/15/1/012. |
[6] |
D. J. Cedio-Fengya, S. Moskow and M. S. Vogelius, Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction, Inverse Problems, 14 (1998), 553-595.
doi: 10.1088/0266-5611/14/3/011. |
[7] |
Y.-S. Chung and S.-Y. Chung, Identification of the combination of monopolar and dipolar sources for elliptic equations, Inverse Problems, 25 (2009), 085006.
doi: 10.1088/0266-5611/25/8/085006. |
[8] |
A. El Badia and T. Ha-Duong, An inverse source problem in potential analysis, Inverse Problems, 16 (2000), 651-663.
doi: 10.1088/0266-5611/16/3/308. |
[9] |
H. Engl, M. Hanke and A. Neubauer, "Regularization of Inverse Problems," Kluwer Academic Publishers, Dordrecht, 1996. |
[10] |
W. B. Gragg and G. D. Johnson, The Laurent-Padé table, In "Information Processing 74, Proceedings IFIP Congress," pages 632-637. North-Holland, Amsterdam, 1974. |
[11] |
M. Hanke, On real-time algorithms for the location search of discontinuous conductivities with one measurement, Inverse Problems, 24 (2008), 045005.
doi: 10.1088/0266-5611/24/4/045005. |
[12] |
M. Hanke, N. Hyvönen, M. Lehn and S. Reusswig, Source supports in electrostatics, BIT, 48 (2008), 245-264.
doi: 10.1007/s10543-008-0172-1. |
[13] |
F. Hettlich and W. Rundell, Iterative methods for the reconstruction of an inverse potential problem, Inverse Problems, 12 (1996), 251-266.
doi: 10.1088/0266-5611/12/3/006. |
[14] |
V. Isakov, "Inverse Problems for Partial Differential Equations," Springer-Verlag, New York, second edition, 2005. |
[15] |
H. Kang and H. Lee, Identification of simple poles via boundary measurements and an application of EIT, Inverse Problems, 20 (2004), 1853-1863.
doi: 10.1088/0266-5611/20/6/010. |
[16] |
O. Kwon, J. K. Seo and J. R. Yoon, A real time algorithm for the location search of discontinuous conductivities with one measurement, Comm. Pure Appl. Math., 55 (2002), 1-29.
doi: 10.1002/cpa.3009. |
show all references
References:
[1] |
L. V. Ahlfors, "Complex Analysis," McGraw-Hill, New York, third edition, 1979. |
[2] |
S. Andrieux and A. Ben Abda, Identification of planar cracks by complete overdetermined data: inversion formulae, Inverse Problems, 12 (1996), 553-563.
doi: 10.1088/0266-5611/12/5/002. |
[3] |
G. A. Baker and P. Graves-Morris, "Padé Approximants," Cambridge University Press, Cambridge, second edition, 1996. |
[4] |
L. Baratchart, A. Ben Abda, F. Ben Hassen and J. Leblond, Recovery of pointwise sources or small inclusions in 2D domains and rational approximation, Inverse Problems, 21 (2005), 51-74.
doi: 10.1088/0266-5611/21/1/005. |
[5] |
L. Baratchart, J. Leblond, F. Mandréa and E. B. Saff, How can the meromorphic approximation help to solve some 2D inverse problems for the Laplacian? Inverse Problems, 15 (1999), 79-90.
doi: 10.1088/0266-5611/15/1/012. |
[6] |
D. J. Cedio-Fengya, S. Moskow and M. S. Vogelius, Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction, Inverse Problems, 14 (1998), 553-595.
doi: 10.1088/0266-5611/14/3/011. |
[7] |
Y.-S. Chung and S.-Y. Chung, Identification of the combination of monopolar and dipolar sources for elliptic equations, Inverse Problems, 25 (2009), 085006.
doi: 10.1088/0266-5611/25/8/085006. |
[8] |
A. El Badia and T. Ha-Duong, An inverse source problem in potential analysis, Inverse Problems, 16 (2000), 651-663.
doi: 10.1088/0266-5611/16/3/308. |
[9] |
H. Engl, M. Hanke and A. Neubauer, "Regularization of Inverse Problems," Kluwer Academic Publishers, Dordrecht, 1996. |
[10] |
W. B. Gragg and G. D. Johnson, The Laurent-Padé table, In "Information Processing 74, Proceedings IFIP Congress," pages 632-637. North-Holland, Amsterdam, 1974. |
[11] |
M. Hanke, On real-time algorithms for the location search of discontinuous conductivities with one measurement, Inverse Problems, 24 (2008), 045005.
doi: 10.1088/0266-5611/24/4/045005. |
[12] |
M. Hanke, N. Hyvönen, M. Lehn and S. Reusswig, Source supports in electrostatics, BIT, 48 (2008), 245-264.
doi: 10.1007/s10543-008-0172-1. |
[13] |
F. Hettlich and W. Rundell, Iterative methods for the reconstruction of an inverse potential problem, Inverse Problems, 12 (1996), 251-266.
doi: 10.1088/0266-5611/12/3/006. |
[14] |
V. Isakov, "Inverse Problems for Partial Differential Equations," Springer-Verlag, New York, second edition, 2005. |
[15] |
H. Kang and H. Lee, Identification of simple poles via boundary measurements and an application of EIT, Inverse Problems, 20 (2004), 1853-1863.
doi: 10.1088/0266-5611/20/6/010. |
[16] |
O. Kwon, J. K. Seo and J. R. Yoon, A real time algorithm for the location search of discontinuous conductivities with one measurement, Comm. Pure Appl. Math., 55 (2002), 1-29.
doi: 10.1002/cpa.3009. |
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