Geodesic
Solution of the linear regression problem using matrix correction methods in the $l_1$ metric
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 2, pp. 202-207 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The linear regression problem is considered as an improper interpolation problem. The metric $l_1$ is used to correct (approximate) all the initial data. A probabilistic justification of this metric in the case of the exponential noise distribution is given. The original improper interpolation problem is reduced to a set of a finite number of linear programming problems. The corresponding computational algorithms are implemented in MATLAB. 
@article{ZVMMF_2016_56_2_a2,
     author = {V. A. Gorelik and O. S. Trembacheva (Barkalova)},
     title = {Solution of the linear regression problem using matrix correction methods in the $l_1$ metric},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {202--207},
     year = {2016},
     volume = {56},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a2/}
}
TY  - JOUR
AU  - V. A. Gorelik
AU  - O. S. Trembacheva (Barkalova)
TI  - Solution of the linear regression problem using matrix correction methods in the $l_1$ metric
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2016
SP  - 202
EP  - 207
VL  - 56
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a2/
LA  - ru
ID  - ZVMMF_2016_56_2_a2
ER  - 
%0 Journal Article
%A V. A. Gorelik
%A O. S. Trembacheva (Barkalova)
%T Solution of the linear regression problem using matrix correction methods in the $l_1$ metric
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 202-207
%V 56
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a2/
%G ru
%F ZVMMF_2016_56_2_a2
V. A. Gorelik; O. S. Trembacheva (Barkalova). Solution of the linear regression problem using matrix correction methods in the $l_1$ metric. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 2, pp. 202-207. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a2/

[1] Barkalova O. S., “Korrektsiya nesobstvennykh zadach lineinogo programmirovaniya v kanonicheskoi forme po minimaksnomu kriteriyu”, Zh. vychisl. matem. i matem. fiz., 52:12 (2012), 2178–2189 | MR | Zbl

[2] Vatolin A. A., “Approksimatsiya nesobstvennykh zadach lineinogo programmirovaniya po kriteriyu evklidovoi normy”, Zh. vychisl. matem. i matem. fiz., 24:12 (1984), 1907–1908 | Zbl

[3] Gorelik V. A., “Matrichnaya korrektsiya zadachi lineinogo programmirovaniya s nesovmestnoi sistemoi ogranichenii”, Zh. vychisl. matem. i matem. fiz., 41:11 (2001), 1697–1705 | MR | Zbl

[4] Gorelik V. A., Erokhin V. I., Optimalnaya matrichnaya korrektsiya nesovmestnykh sistem lineinykh algebraicheskikh uravnenii po minimumu evklidovoi normy, VTs RAN, M., 2004 | MR

[5] Gorelik V. A., Erokhin V. I., Pechenkin R. V., Chislennye metody korrektsii nesobstvennykh zadach lineinogo programmirovaniya i strukturnykh sistem uravnenii, VTs RAN, M., 2006 | MR

[6] Erokhin V. I., Krasnikov A. S., Khvostov M. N., “Minimalnye po evklidovoi norme matrichnye korrektsii zadach lineinogo programmirovaniya”, Avtomatika i telemekhanika, 2012, no. 2, 11–24

[7] Back A., “The matrix-restricted total least squares problem”, Signal Process, 87:10 (2007), 2303–2312 | DOI

[8] Golub G. H., Van Loan C. F., “An analysis of the total least squares problem”, SIAM J. Numer. Anal., 17:3 (1980), 883–893 | DOI | MR | Zbl

[9] Rosen J. B., Park H., Glick J., “Total least norm formulation and solution for strucured problems”, SIAM J. Matrix Anal. Appl., 17:1 (1996), 110–128 | DOI | MR

[10] Van Huffel S., Vandewale J., The total least squares problems: computational aspects and analysis, Frontiers in Applied Mathematics, 9, SIAM Publishing, Philadelphia, PA | MR

[11] Antipin A. S., Vasilev F. P., “Regulyarizovannyi metod s prognozom dlya resheniya variatsionnykh neravenstv s netochno zadannym mnozhestvom”, Zh. vychisl. matem. i matem. fiz., 44:5 (2004), 796–804 | MR | Zbl

[12] Matrosov V. L., Gorelik V. A., Zhdanov S. A., Muraveva O. V., Ugolnikova B. Z., Teoreticheskie osnovy informatiki, Uchebnoe posobie dlya studentov vuzov, Izdatelskii tsentr “Akademiya”, M., 2009

[13] Shiryaev A. N., Osnovy stokhasticheskoi finansovoi matematiki, v. 1, Fakty. Modeli, Fazis, M., 1998

[14] Gorelik V. A., Zolotova T. V., “Ob ekvivalentnosti printsipov optimalnosti investitsionnogo portfelya”, Nauchno-issledovatelskii finansovyi institut. Finansovyi zhurnal, 2014, no. 2(20), 67–74