Geodesic
The self-organization models of various base forming
Matematičeskoe modelirovanie, Tome 14 (2002) no. 10, pp. 43-58 
V. M. Balyk; D. P. Kostomarov; V. I. Kukulin; K. A. Shishaev. The self-organization models of various base forming. Matematičeskoe modelirovanie, Tome 14 (2002) no. 10, pp. 43-58. http://geodesic.mathdoc.fr/item/MM_2002_14_10_a3/
@article{MM_2002_14_10_a3,
     author = {V. M. Balyk and D. P. Kostomarov and V. I. Kukulin and K. A. Shishaev},
     title = {The self-organization models of various base forming},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {43--58},
     year = {2002},
     volume = {14},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2002_14_10_a3/}
}
TY  - JOUR
AU  - V. M. Balyk
AU  - D. P. Kostomarov
AU  - V. I. Kukulin
AU  - K. A. Shishaev
TI  - The self-organization models of various base forming
JO  - Matematičeskoe modelirovanie
PY  - 2002
SP  - 43
EP  - 58
VL  - 14
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/MM_2002_14_10_a3/
LA  - ru
ID  - MM_2002_14_10_a3
ER  - 
%0 Journal Article
%A V. M. Balyk
%A D. P. Kostomarov
%A V. I. Kukulin
%A K. A. Shishaev
%T The self-organization models of various base forming
%J Matematičeskoe modelirovanie
%D 2002
%P 43-58
%V 14
%N 10
%U http://geodesic.mathdoc.fr/item/MM_2002_14_10_a3/
%G ru
%F MM_2002_14_10_a3

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

A new way in forming a various base, that is used in simulation complex boundary problems is discussed. The optimum structure of the basis functions is chosen on the base of the principles of the self-organization of the complex systems theory, that let us make algorithms in forming basis functions simple enough. The new operations under the statistical samples are introduced. This reduces to an absolutely new algorithms of solving many-dimensional and optimization problems. The practice convergence of the self-organization method is shown in the model test.

[1] Kukulin V. I., Izvestiya AN SSSR, ser.fiz., 39:3 (1975), 535–542

[2] Krasnopolskii V. M., Kukulin. V. I., Izvestiya AN SSSR, ser. fiz., 39:3 (1975), 543

[3] Burilov A. A., Kostomarov D. P., Kukulin V. I., “Stokhasticheskii metod optimizatsii neminimalnogo variatsionnogo bazisa”, Matem. modelirovanie, 12:1 (2000), 104–113 | Zbl

[4] Kukulin V. I., Krasnopolsky V. M., J. Phys, G3 (1977), 795

[5] Varga K., Suzuki Y., Stochastic variational method, Springer Verlag, Heidelberg, 1998 | MR

[6] Varga K., Suzuki Y., Lovas R. G., Nucl. Phys. A, 571 (1994), 447 | DOI

[7] Kostomarov D. P., Kukulin V. I., Sazonov P. B., Vestnik MGU, ser. 15, Vychislit. matematika i kibernetika, 1984, no. 1, 3 | MR | Zbl

[8] Kachman S., Shtengauz G., Teoriya ortogonalnykh ryadov, Fizmatgiz, M., 1958 | MR

[9] Aleksidze M. A., Reshenie granichnykh zadach metodom razlozheniya po neortogonalnym funktsiyam, Nauka, M., 1978 | MR | Zbl

[10] Ivakhnenko A. G., Induktivnyi metod samoorganizatsii modelei slozhnykh sistem, Nauka, Kiev, 1981

[11] Ivakhnenko A. G., Dolgosrochnoe prognozirovanie i upravlenie slozhnymi sistemami, Tekhnika, Kiev, 1975

[12] Ivakhnenko A. G., Samoorganizatsiya sistemy raspoznavaniya i avtomaticheskogo upravleniya, Tekhnika, Kiev, 1966

[13] Widrow B., Generalization and information storage in networks of adaline neurons on self – organizing systems, Spartan Books, Washington, DC, 1962

[14] Linnik Yu. V., Metod naimenshikh kvadratov i osnovy matematiko-statisticheskoi obrabotki nablyudenii, Fizmatgiz, 1962

[15] Balyk V. M., Astronavtika i raketodinamika, 1999, no. 21–22

[16] Landau L. D., Lifshits E. M., Kvantovaya mekhanika, Izd. 2-oe, Fizmatgiz, M., 1963 | MR