Numerical methods for some inverse problems of heart electrophysiology

Differential Equations

Volumn 45, Issue 7, 2009, Pages 1034-1043

  Denisov, A M ^a,b   Zakharov, E V ^a,b   Kalinin, A V ^a,b   Kalinin, V V ^a,b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b INSTITUTE OF BIOMEDICAL CHEMISTRY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77749321314     PISSN: 00122661     EISSN: None     Source Type: Journal    
DOI: 10.1134/S0012266109070106     Document Type: Article

References (12)

1. MacLeod, R. S. and Brooks, D. H., Recent Progress in Inverse Problems in Electrocardiology, IEEE Eng. in Med. Bio. Mag., 1998, vol. 17, no. 1, pp. 73-83.
2. Babaeizadeh, S. and Brooks, D. H., Electrical Impedance Tomography for Piecewise Constant Domains Using Boundary Element Shape-Based Inverse Solutions, IEEE Trans. on Medical Imaging, 2007, vol. 26, no. 5, pp. 637-647.
3. Lavrent'ev, M. M., Romanov, V. G., and Shishatskii, S. P., Nekorrektnye zadachi matematicheskoi fiziki i analiza (Ill-Posed Problems of Mathematical Physics and Analysis), Moscow, 1980.
4. Landis, E. M., Some Questions in the Qualitative Theory of Elliptic and Parabolic Equations, Uspekhi Mat. Nauk, 1959, vol. 14, no. 1, pp. 21-85.
5. Lattes, R. and Lions, J.-L., Méthode de quasi-réversibilité et applications, Paris: Dunod, 1967. Translated under the title Metod kvaziobrashcheniya i ego prilozheniya, Moscow: Mir, 1970.
6. Kozlov, V. A., Maz'ya, V. G., and Fomin, A. V., An Iterative Method for Solving the Cauchy Problem for Elliptic Equations, Zh. Vychisl. Mat. Mat. Fiz., 1991, vol. 31, no. 1, pp. 64-74.
7. Samarskii, A. A. and Vabishchevich, P. N., Chislennye metody resheniya obratnykh zadach matematicheskoi fiziki (Numerical Methods for the Solution of Inverse Problems of Mathematical Physics), Moscow, 2004.
8. Denisov, A. M., Zakharov, E. V., Kalinin, A. V., Kalinin, V. V., Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 2008, no. 2, pp. 5-10.
9. Tikhonov, A. N. and Arsenin, V. Ya., Metody resheniya nekorrektnykh zadach (Methods for the Solution of Ill-Posed Problems), Moscow: Nauka, 1979.
10. Dihn Nho Hào and Lesnic, D., The Cauchy Problem for Laplace's Equation via the Conjugate Gradient Method, IMA J. Appl. Math., 2000, no. 65, pp. 199-217.
11. Tikhonov, A. N. and Samarskii, A. A., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Izd. Moskov. Univ., 1999.
12. Zakharov, E. V. and Kalinin, A. V., Numerical Solution of the Dirichlet Three-Dimensional Problem in a Piecewise Homogeneous Medium by the Method of Boundary Integral Equations, Zh. Vychisl. Mat. Mat. Fiz., 2009, vol. 49, no. 7, pp. 856-872.