Geodesic
A~correct flow chart for numerical solution to an inverse problem by optimization method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 2, pp. 139-149.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, two flow charts for solving the same inverse problem by an optimization method are presented. On numerical examples it is shown that the first flow chat often used by researchers requires much more computer costs than the second one. This is because of the necessity of using a fine net and due to an increase in the number of minimization iterations of the residual functional for its decrease up to a certain value. 
@article{SJVM_2008_11_2_a2,
     author = {A. L. Karchevsky},
     title = {A~correct flow chart for numerical solution to an inverse problem by optimization method},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {139--149},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2008_11_2_a2/}
}
TY  - JOUR
AU  - A. L. Karchevsky
TI  - A~correct flow chart for numerical solution to an inverse problem by optimization method
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2008
SP  - 139
EP  - 149
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2008_11_2_a2/
LA  - ru
ID  - SJVM_2008_11_2_a2
ER  - 
%0 Journal Article
%A A. L. Karchevsky
%T A~correct flow chart for numerical solution to an inverse problem by optimization method
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2008
%P 139-149
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2008_11_2_a2/
%G ru
%F SJVM_2008_11_2_a2
A. L. Karchevsky. A~correct flow chart for numerical solution to an inverse problem by optimization method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 2, pp. 139-149. http://geodesic.mathdoc.fr/item/SJVM_2008_11_2_a2/

[1] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981 | MR

[2] Romanov V. G., Obratnye zadachi matematicheskoi fiziki, Nauka, M., 1984 | MR

[3] Karchevskii A. L., “O povedenii funktsionala nevyazki dlya odnomernoi giperbolicheskoi obratnoi zadachi”, Sib. zhurn. vychisl. matematiki, 2:2 (1999), 137–160 | MR

[4] Karchevsky A. L., “Properties of the misfit functional for a nonlinear one-dimentioanal coefficient hyperbolic inverse problem”, J. of Inverse and Ill-posed Problems, 5:2 (1997), 139–163 | DOI | MR | Zbl

[5] Karchevsky A. L., “Finite-difference coefficient inverse problem and properties of the misfit functional”, J. of Inverse and Ill-Posed Problems, 6:5 (1998), 431–452 | DOI | MR | Zbl