Some interval problems of the theory of discrete linear systems
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 5 (2005) no. 1, pp. 129-137.

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

Artificial neural networks can be used effectively for а quite general class of problems. Still there exists nо formal foundation of some important constructions used in the theory. ln this paper аn attempt is undertaken to formalize some concepts of neuroinformatics аnd consider their properties from the point of view of applied universal algebra. lt is proposed to treat neural networks as heterogeneous algebras which has made it possible to prove for them basic results similar to algebraic theorems оn homomorphisms аnd congruences.
@article{ISU_2005_5_1_a12,
     author = {D. V. Speranskiy and L. V. Kupriyanova},
     title = {Some interval problems of the theory of discrete linear systems},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {129--137},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2005_5_1_a12/}
}
TY  - JOUR
AU  - D. V. Speranskiy
AU  - L. V. Kupriyanova
TI  - Some interval problems of the theory of discrete linear systems
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2005
SP  - 129
EP  - 137
VL  - 5
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2005_5_1_a12/
LA  - ru
ID  - ISU_2005_5_1_a12
ER  - 
%0 Journal Article
%A D. V. Speranskiy
%A L. V. Kupriyanova
%T Some interval problems of the theory of discrete linear systems
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2005
%P 129-137
%V 5
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2005_5_1_a12/
%G ru
%F ISU_2005_5_1_a12
D. V. Speranskiy; L. V. Kupriyanova. Some interval problems of the theory of discrete linear systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 5 (2005) no. 1, pp. 129-137. http://geodesic.mathdoc.fr/item/ISU_2005_5_1_a12/

[1] Zade L., Dezoer Ch., Teoriya lineinykh sistem, M., 1970

[2] Kalman R., Falb P., Arbib M., Ocherki po matematicheskoi teorii sistem, M., 1971 | MR

[3] Fomin V. N., Metody upravleniya lineinymi diskretnymi ob'ektami, L., 1985

[4] Alefeld G., Khertsberger Yu., Vvedenie v intervalnye vychisleniya, M., 1987 | MR

[5] Kalmykov S. A., Shokin Yu. I., Yuldashev Z. Kh., Metody intervalnogo analiza, Novosibirsk, 1986 | MR

[6] Sharyi S. P., Intervalnye algebraicheskie zadachi i ikh chislennoe reshenie, Dis. ... d-ra fiz.-mat. nauk, Novosibirsk, 2000

[7] Gill A., Lineinye posledovatelnostnye mashiny, M., 1974

[8] Pervozvanskii A. A., Kurs teorii avtomaticheskogo upravleniya, M., 1986

[9] Kupriyanova L., “Inner estimation of the united solution set of interval linear algebraic system”, Reliale Computing, 1:1 (1995), 15–31 | DOI | MR | Zbl

[10] Collats L., Funktionalanalysis und Numerische Mathematik, Berlin–Göttingen–Heidelberg, 1964