Geodesic
Algebra over estimation algorithms: Normalization and division
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 6, pp. 1099-1109 
A. G. D'yakonov. Algebra over estimation algorithms: Normalization and division. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 6, pp. 1099-1109. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_6_a13/
@article{ZVMMF_2007_47_6_a13,
     author = {A. G. D'yakonov},
     title = {Algebra over estimation algorithms: {Normalization} and division},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1099--1109},
     year = {2007},
     volume = {47},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_6_a13/}
}
TY  - JOUR
AU  - A. G. D'yakonov
TI  - Algebra over estimation algorithms: Normalization and division
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 1099
EP  - 1109
VL  - 47
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_6_a13/
LA  - ru
ID  - ZVMMF_2007_47_6_a13
ER  - 
%0 Journal Article
%A A. G. D'yakonov
%T Algebra over estimation algorithms: Normalization and division
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 1099-1109
%V 47
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_6_a13/
%G ru
%F ZVMMF_2007_47_6_a13

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

An algebra over recognition algorithms supplemented with a normalization operation (under various definitions) and the division operation is investigated. Correctness criteria for various algebraic closures are obtained.

[1] Zhuravlev Yu. I., “Korrektnye algoritmy nad mnozhestvami nekorrektnykh (evristicheskikh) algoritmov. II”, Kibernetika, 1977, no. 6, 21–27 | Zbl

[2] Zhuravlev Yu. I., “Ob algebraicheskom podkhode k resheniyu zadach raspoznavaniya ili klassifikatsii”, Probl. kibernetiki, 33, Nauka, M., 1978, 5–68

[3] Dyakonov A. G., “Algebra nad algoritmami vychisleniya otsenok: minimalnaya stepen korrektnogo algoritma”, Zh. vychisl. matem. i matem. fiz., 45:6 (2005), 1134–1145 | MR

[4] Zhuravlev Yu. I., Nikiforov V. V., “Algoritmy raspoznavaniya, osnovannye na vychislenii otsenok”, Kibernetika, 1971, no. 3, 1–11 | Zbl

[5] Dyakonov A. G., “Algebra nad algoritmami vychisleniya otsenok: monotonnye reshayuschie pravila”, Zh. vychisl. matem. i matem. fiz., 45:10 (2005), 1893–1904 | MR

[6] Ilin V. A., Kim G. D., Lineinaya algebra i analiticheskaya geometriya: Uchebnik, Izd-vo Mosk. un-ta, M., 1998

[7] Matrosov B. L., “O kriteriyakh polnoty modeli algoritmov vychisleniya otsenok i ee algebraicheskikh zamykanii”, Dokl. AN SSSR, 258:4 (1981), 791–796 | MR

[8] Matrosov B. L., “Korrektnye algebry ogranichennoi emkosti nad mnozhestvom algoritmov vychisleniya otsenok”, Zh. vychisl. matem. i matem. fiz., 21:5 (1981), 1276–1291 | MR | Zbl

[9] Proskuryakov I. V., Sbornik zadach po lineinoi algebre, Nauka, M., 1970

[10] Dyakonov A. G., Algebra nad algoritmami vychisleniya otsenok: Uchebnoe posobie, Izdatelskii otdel f-ta VMiK MGU, M., 2006

[11] Micchelli C. A., “Interpolation of scattered data: Distance matrices and conditionally positive definite functions”, Construct. Aproximat., 2 (1986), 11–22 | DOI | MR | Zbl