Algebra over estimation algorithms: the minimal degree of correct algorithms
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 6, pp. 1134-1145 Cet article a éte moissonné depuis la source Math-Net.Ru

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Basic constructs of the algebraic theory of corrections of estimation algorithms are described. Algorithms belonging to algebraic closures are represented using linear combinations of simple operators. The case of the general proximity function is considered, and an unimprovable bound on the degree of a correct algorithm is obtained.
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A. G. D'yakonov. Algebra over estimation algorithms: the minimal degree of correct algorithms. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 6, pp. 1134-1145. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_6_a14/

[1] Zhuravlev Yu. I., “Korrektnye algoritmy nad mnozhestvami nekorrektnykh (evristicheskikh) algoritmov, I”, Kibernetika, 1977, no. 4, 5–17 | Zbl

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

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

[4] Matrosov V. L., Korrektnye algebry algoritmov raspoznavaniya ogranichennoi emkosti, Dis. ...dokt. fiz.-matem. nauk, Gos. ped. in-t, M., 1985

[5] Plokhonina T. V., “O nekorrektnosti algebraicheskogo zamykaniya vtoroi stepeni semeistva algoritmov vychisleniya otsenok”, Zh. vychisl. matem. i matem. fiz., 25:7 (1985), 1078–1085 | MR | Zbl

[6] Rudakov K. V., “Ob algebraicheskoi teorii universalnykh i lokalnykh ogranichenii dlya zadach klassifikatsii”, Raspoznavanie, klassifikatsiya, prognoz, 1, Nauka, M., 1989, 176–201 | MR

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

[8] Dyakonov A. G., “O vybore sistemy opornykh mnozhestv dlya effektivnoi realizatsii algoritmov raspoznavaniya tipa vychisleniya otsenok”, Zh. vychisl. matem. i matem. fiz., 40:7 (2000), 1104–1118 | MR

[9] Riordan Dzh., Kombinatornye tozhdestva, Nauka, M., 1982 | MR | Zbl

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

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

[12] Bak Khyng Kkhang, Issledovanie modelei raspoznayuschikh operatorov i ikh lineinykh i algebraicheskikh zamykanii, Dis. ...dokt. fiz.-matem. nauk, VTs AN SSSR, M., 1979, 251 pp.

[13] Rudakov K. V., Algebraicheskaya teoriya universalnykh i lokalnykh ogranichenii dlya algoritmov raspoznavaniya, Dis. ...dokt. fiz.-matem. nauk, VTs RAN, M., 1992