Geodesic
On the consistency of linear and quadratic systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 563-567 
A. V. Arutyunov; E. V. Kruglova. On the consistency of linear and quadratic systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 563-567. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a0/
@article{ZVMMF_2006_46_4_a0,
     author = {A. V. Arutyunov and E. V. Kruglova},
     title = {On the consistency of linear and quadratic systems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {563--567},
     year = {2006},
     volume = {46},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a0/}
}
TY  - JOUR
AU  - A. V. Arutyunov
AU  - E. V. Kruglova
TI  - On the consistency of linear and quadratic systems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 563
EP  - 567
VL  - 46
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a0/
LA  - ru
ID  - ZVMMF_2006_46_4_a0
ER  - 
%0 Journal Article
%A A. V. Arutyunov
%A E. V. Kruglova
%T On the consistency of linear and quadratic systems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 563-567
%V 46
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a0/
%G ru
%F ZVMMF_2006_46_4_a0

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

A system of linear inhomogeneous inequalities is examined. An algorithm is presented for isolating all the consistent subsystems in this system that are maximal with respect to inclusion, and justification of this algorithm is given. A criterion for the consistency of a system of quadratic inhomogeneous equations and inequalities is proposed.

[1] Zhuravlev Yu. I., “Ob algebraicheskom podkhode k resheniyu zadach raspoznavaniya ili klassifikatsii”, Probl. kibernetiki, 33 (1978), 6–58

[2] Zhuravlev Yu. I., Miroshnik C. H., Shvartin S. M., “Ob odnom podkhode k optimizatsii v klasse parametricheskikh algoritmov raspoznavaniya”, Zh. vychisl. matem. i matem. fiz., 16:1 (1976), 209–218 | MR | Zbl

[3] Yu. I. Zhuravlev (red.), Raspoznavanie. Klassifikatsiya. Prognoz, Nauka, M., 1988

[4] Ryazanov V. V., “Optimizatsiya algoritmov vychisleniya otsenok po parametram, kharakterizuyuschim predstavitelnost etalonnykh strok”, Zh. vychisl. matem. i matem. fiz., 16:6 (1976), 1559–1570 | MR | Zbl

[5] Eremin I. I., Mazurov V. D., Astafev H. H., Nesobstvennye zadachi lineinogo i vypuklogo programmirovaniya, Nauka, M., 1983 | MR

[6] Ashmanov S. A., Lineinoe programmirovanie, Nauka, M., 1981 | Zbl

[7] Arutyunov A. B., Usloviya ekstremuma. Anormalnye i vyrozhdennye zadachi, Faktorial, M., 1997 | MR | Zbl

[8] Arutyunov A. B., Yachimovich V., “K teorii anormalnykh ekstremalnykh zadach”, Vestn. MGU. Ser. Vychisl. matem. i kibernetika, 2000, no. 1, 34–40 | MR | Zbl