Geodesic
The asymptotic behaviour of the $s$-step method of steepest descent for minimizing a quadratic functional in Hilbert space
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 35 (1995) no. 2, pp. 163-177 
P. F. Zhuk. The asymptotic behaviour of the $s$-step method of steepest descent for minimizing a quadratic functional in Hilbert space. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 35 (1995) no. 2, pp. 163-177. http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_2_a0/
@article{ZVMMF_1995_35_2_a0,
     author = {P. F. Zhuk},
     title = {The asymptotic behaviour of the $s$-step method of steepest descent for minimizing a quadratic functional in {Hilbert} space},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {163--177},
     year = {1995},
     volume = {35},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_2_a0/}
}
TY  - JOUR
AU  - P. F. Zhuk
TI  - The asymptotic behaviour of the $s$-step method of steepest descent for minimizing a quadratic functional in Hilbert space
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1995
SP  - 163
EP  - 177
VL  - 35
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_2_a0/
LA  - ru
ID  - ZVMMF_1995_35_2_a0
ER  - 
%0 Journal Article
%A P. F. Zhuk
%T The asymptotic behaviour of the $s$-step method of steepest descent for minimizing a quadratic functional in Hilbert space
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1995
%P 163-177
%V 35
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_2_a0/
%G ru
%F ZVMMF_1995_35_2_a0

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

[1] Kantorovich L. V., “Funktsionalnyi analiz i prikladnaya matematika”, Uspekhi matem. nauk, 3:6 (1948), 89–185 | MR | Zbl

[2] Forsythe G. E., Motzkin T. S., “Asymptotic properties of the optimum gradient method (abstract)”, Bull. Amer. Math. Soc., 57:2 (1951), 183

[3] Akaike H., “On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method”, Ann. Inst. Statist. Math. Tokyo, 11 (1959), 1–16 | DOI | MR | Zbl

[4] Forsythe G. E., “On the asymptotic directions of the s-dimensional optimum gradient method”, Numer. Math., 11:1 (1968), 57–76 | DOI | MR | Zbl

[5] Zabolotskaya A. F., “Asimptoticheskoe povedenie $s$-shagovogo metoda skoreishego spuska v gilbertovom prostranstve”, Zh. vychisl. matem. i matem. fiz., 19:1 (1979), 228–232 | MR | Zbl

[6] Zabolotskaya A. F., “Uskorenie skhodimosti metoda skoreishego spuska v gilbertovom prostranstve”, Zh. vychisl. matem. i matem fiz., 14:1 (1974), 218–221

[7] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR

[8] Zhuk P. F., Bondarenko L. N., “Ob odnoi gipoteze Dzh. Forsaita”, Matem. sb., 121:4 (1983), 435–453 | MR

[9] Akhiezer N. I., Glazman I. M., Teoriya lineinykh operatorov v gilbertovom prostranstve, v. 1, Vischa shkola, Kharkov, 1977

[10] Geronimus Ya. L., Teoriya ortogonalnykh mnogochlenov, Gostekhteorizdat, M., 1950

[11] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR

[12] Ostrowski A. M., Solution of equations and systems of equations, Acad. Press, N. Y.-L., 1966 | MR