О сложности градиента рациональной функции
Diskretnyj analiz i issledovanie operacij, Tome 14 (2007) no. 4, pp. 57-75.

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

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I. S. Sergeev. О сложности градиента рациональной функции. Diskretnyj analiz i issledovanie operacij, Tome 14 (2007) no. 4, pp. 57-75. http://geodesic.mathdoc.fr/item/DA_2007_14_4_a4/

[1] Gashkov S. B., “Zamechanie o minimizatsii glubiny bulevykh skhem”, Vestnik MGU. Ser. 1. Matematika. Mekhanika, 2007, no. 3, 7–9

[2] Gashkov S. B., Gashkov I. B., “O slozhnosti vychisleniya differentsialov i gradientov”, Diskr. matem., 17:3 (2005), 45–67 | MR | Zbl

[3] Gashkov S. B., Kochergin V. V., “Ob additivnykh tsepochkakh vektorov, ventilnykh skhemakh i slozhnosti vychisleniya stepenei”, Metody diskretnogo analiza v teorii grafov i slozhnosti, Sb. nauch. tr. Vyp. 52, Institut matematiki, Novosibirsk, 1992, 22–40 | MR

[4] Kim K. V., Nesterov Yu. E., Cherkasskii B. V., “Otsenka trudoemkosti vychisleniya gradienta”, Dokl. AN SSSR, 275:6 (1984), 1306–1309 | MR | Zbl

[5] Lozhkin S. A., “O svyazi mezhdu glubinoi i slozhnostyu ekvivalentnykh formul i o glubine monotonnykh funktsii algebry logiki”, Problemy kibernetiki, Vyp. 38, Nauka, M., 1981, 269–271 | MR

[6] Lupanov O. B., “O ventilnykh i kontaktno-ventilnykh skhemakh”, Dokl. AN SSSR, 111:6 (1956), 1171–1174 | MR | Zbl

[7] Baur W., Strassen V., “The complexity of partial derivatives”, Theoret. Comput. Sci., 22 (1983), 317–330 ; Baur V., Shtrassen F., “Slozhnost chastnykh proizvodnykh”, Kiberneticheskii sbornik (Novaya seriya), Vyp. 22, Mir, M., 1985, 3–18 | DOI | MR | Zbl | MR

[8] Bernstein D. J., The transposition principle, http://cr.yp.to/transposition.html

[9] Bostan A., Lecerf G., Schost E., “Tellegen's principle into practice”, ISSAC Conf., (Philadelphia, 2003), ACM Press, Philadelphia, 37–44 | Zbl

[10] Fiduccia C. M., On the algebraic complexity of matrix multiplication, Ph. D. thesis, Brown Univ., 1973

[11] Hoover H., Klawe M., Pippenger N., “Bounding fan-out in logical networks”, J. Assoc. Comput. Mach., 31:1 (1984), 13–18 | MR | Zbl

[12] Kaltofen E., Shoup V., “Subquadratic-time factoring of polynomials over finite fields”, Math. Comput., 67:223 (1998), 1179–1197 | DOI | MR | Zbl

[13] Kaltofen E., Singer M., “Size efficient parallel algebraic circuits for partial derivatives”, IV ICCAPR Conf. Singapore, 1991, 133–145

[14] Linnainmaa S., “Taylor expansion of the accumulated rounding error”, BIT, 16:2 (1976), 146–160 | DOI | MR | Zbl

[15] Morgenstern J., “How to compute fast a function and all its derivations”, SIGACT News, 16:4 (1985), 60–62 | DOI

[16] Reif J., Tate S., “Optimal size integer division circuits”, SIAM J. Comput., 19:5 (1990), 912–925 | DOI | MR

[17] Strassen V., “Vermeidung von divisionen”, J. für die reine und angewandte Math., 264 (1973), 184–202 | MR | Zbl