Geodesic
Uncertainty estimation of the method based on generalized residual principle for the restore task of the spectral density of crystals
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 2, pp. 25-30 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article studies the task of identification of phonon spectrum of a crystal according to its hit capacity. The authors reveal the evaluation of accuracy of Tikhonov regularization method with regularization parameter which was chosen form generalized residual principle.
Keywords: regularization; module of continuity; uncertainty estimation; ill-conditioned task; generalized residual principle. 
@article{VYURM_2015_7_2_a2,
     author = {A. A. Ershova and A. I. Sidikova},
     title = {Uncertainty estimation of the method based on generalized residual principle for the restore task of the spectral density of crystals},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {25--30},
     year = {2015},
     volume = {7},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2015_7_2_a2/}
}
TY  - JOUR
AU  - A. A. Ershova
AU  - A. I. Sidikova
TI  - Uncertainty estimation of the method based on generalized residual principle for the restore task of the spectral density of crystals
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
PY  - 2015
SP  - 25
EP  - 30
VL  - 7
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VYURM_2015_7_2_a2/
LA  - ru
ID  - VYURM_2015_7_2_a2
ER  - 
%0 Journal Article
%A A. A. Ershova
%A A. I. Sidikova
%T Uncertainty estimation of the method based on generalized residual principle for the restore task of the spectral density of crystals
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
%D 2015
%P 25-30
%V 7
%N 2
%U http://geodesic.mathdoc.fr/item/VYURM_2015_7_2_a2/
%G ru
%F VYURM_2015_7_2_a2
A. A. Ershova; A. I. Sidikova. Uncertainty estimation of the method based on generalized residual principle for the restore task of the spectral density of crystals. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 2, pp. 25-30. http://geodesic.mathdoc.fr/item/VYURM_2015_7_2_a2/

[1] Lifshits I. M., Zhurnal eksperimental'noy i teoreticheskoy fiziki, 26:5 (1954), 551–556 (in Russ.)

[2] Tanana V. P., Erygina A. A., Sibirskiy zhurnal industrial'noy matematiki, 17:2(58) (2014), 125–136 (in Russ.)

[3] Tanana V. P., Sidikova A. I., Vishnyakov E. Yu., “On Error Estimates for Regularizing Algorithm Based on Generalized Residual Method when Solving Integral Equations”, Bulletin of South Ural State University. Series of “Computer Technologies, Automatic Control Radioelectronics”, 14:4 (2014), 59–64 (in Russ.)

[4] Tanana V. P., Boyarshinov V. V., Dep. v VINITI, 892-V87, 1987 (in Russ.)

[5] Tikhonov A. N., Dokl. AN SSSR, 151:3 (1963), 501–504 (in Russ.)

[6] Goncharskiy A. V., Leonov A. S., Yagola A. G., Zhurnal vychislitel'noy matematiki i matematicheskoy fiziki, 13:2 (1973), 294–302 (in Russ.)

[7] Tanana V. P., Dokl. AN SSSR, 224:15 (1975), 1025–1029 (in Russ.)

[8] Tanana V. P., Methods of solution of operator equations, Nauka Publ., M., 1981, 156 pp. (in Russ.)