Geodesic
Dual systems of homogeneous linear equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 48-53 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The notion of dual system of homogeneous linear algebraic equations is introduced. A modification of the Gaussian elimination method for the simultaneous solution of primal and dual systems is proposed. An algorithm for solving a homogeneous system of linear equations is validated. The algorithm is based on the technique of the dual representation of the polyhedral cone and, thus, is dual to the known Gauss–Jordan method.
Keywords: dual systems, linear algebraic equations, Gaussian elimination method, dual method, polyhedral cone. 
@article{TIMM_2013_19_2_a4,
     author = {N. N. Astaf'ev},
     title = {Dual systems of homogeneous linear equations},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {48--53},
     year = {2013},
     volume = {19},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a4/}
}
TY  - JOUR
AU  - N. N. Astaf'ev
TI  - Dual systems of homogeneous linear equations
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2013
SP  - 48
EP  - 53
VL  - 19
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a4/
LA  - ru
ID  - TIMM_2013_19_2_a4
ER  - 
%0 Journal Article
%A N. N. Astaf'ev
%T Dual systems of homogeneous linear equations
%J Trudy Instituta matematiki i mehaniki
%D 2013
%P 48-53
%V 19
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a4/
%G ru
%F TIMM_2013_19_2_a4
N. N. Astaf'ev. Dual systems of homogeneous linear equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 48-53. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a4/

[1] Takker A. U., “Dvoistvennye sistemy odnorodnykh lineinykh sootnoshenii”, Lineinye neravenstva i smezhnye voprosy, Cb. st., eds. G. Kun, A. Takker, IL, M., 1959, 127–141

[2] Goldman A. Dzh., Takker A. U., “Mnogogrannye vypuklye konusy”, Lineinye neravenstva i smezhnye voprosy, Cb. st., eds. G. Kun, A. Takker, IL, M., 1959, 142–161

[3] Chernikov S. N., Lineinye neravenstva, Nauka, M., 1968, 468 pp. | MR | Zbl

[4] Eremin I. I., Lineinaya optimizatsiya i sistemy lineinykh neravenstv, Izd. tsentr “Akademiya”, M., 2007, 249 pp.

[5] Eremin I. I., Dvoistvennost dlya nesobstvennykh zadach matematicheskogo programmirovaniya, UNTs AN SSSR, Sverdlovsk, 1981, 43 pp.

[6] Eremin I. I., Mazurov Vl. D., Astafev N. N., Nesobstvennye zadachi lineinogo i vypuklogo programmirovaniya, Nauka, M., 1983, 336 pp. | MR

[7] Gantmakher F. R., Teoriya matrits, Nauka, M., 1966, 580 pp. | MR

[8] Bakhvalov N. S., Chislennye metody, v. I, Nauka, M., 1973, 632 pp. | MR | Zbl

[9] Streng G., Lineinaya algebra i ee primenenie, Mir, M., 1980, 456 pp.

[10] Murtaf B., Sovremennoe lineinoe programmirovanie, Mir, M., 1976, 224 pp. | MR

[11] Zukhovitskii S. I., Avdeeva L. I., Lineinoe i vypukloe programmirovanie, Nauka, M., 1967, 490 pp. | MR

[12] Rokafellar R., Vypuklyi analiz, Mir, M., 1973, 470 pp.

[13] Bellman R., Vvedenie v teoriyu matrits, Nauka, M., 1976, 352 pp. | MR

[14] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989, 655 pp. | MR