Probabilistic analyses of the plain multiple gcd algorithm

Journal of Symbolic Computation - Tập 74 - Trang 425-474 - 2016
Valérie Berthé1, Loïck Lhote2, Brigitte Vallée3
1LIAFA, UMR CNRS 7089, Université Paris Diderot, France
2GREYC, UMR CNRS 6072, ENSICAEN & Université de Caen Normandie, France
3GREYC, UMR CNRS 6072, Université de Caen Normandie, France

Tài liệu tham khảo

Akhavi, 2009, On the reduction of a random basis, ESAIM Probab. Stat., 13, 437, 10.1051/ps:2008012 Baladi, 2005, Euclidean algorithms are Gaussian, J. Number Theory, 110, 331, 10.1016/j.jnt.2004.08.008 Berthé, 2013, Multiple gcds. probabilistic analysis of the plain algorithm, 37 Berthé, 2000, On continued fraction expansions in positive characteristic: equivalence relations and some metric properties, Expo. Math., 18, 257 Brent, 1976, Analysis of the binary Euclidean algorithm, 321 Dixon, 1970, The number of steps in the Euclidean algorithm, J. Number Theory, 2, 414, 10.1016/0022-314X(70)90044-2 Edwards, 2001 Flajolet, 2009 Flajolet, 1998, Continued fraction algorithms, functional operators, and structure constants, Theor. Comput. Sci., 194, 1, 10.1016/S0304-3975(97)00123-0 Friesen, 1996, The statistics of continued fractions for polynomials over a finite field, Proc. Am. Math. Soc., 124, 2661, 10.1090/S0002-9939-96-03394-1 Heilbronn, 1969, On the average length of a class of continued fractions, 87 Hensley, 1994, The number of steps in the Euclidean algorithm, J. Number Theory, 2, 149 Knopfmacher, 1988, The exact length of the Euclidean algorithm in Fq[X], Mathematika, 35, 297, 10.1112/S002557930001528X Knuth, 1998, Seminumerical Algorithms, vol. 2 Landau, 1924, Über die Anzahl der Gitterpunkte in gewissen Bereichen. IV, Nachr. Ges. Wiss. Gött., Math.-Phys. Kl., 1924, 137 Lhote, 2008, Gaussian laws for the main parameters of the Euclid algorithms, Algorithmica, 50, 497, 10.1007/s00453-007-9009-6 Ma, 1990, Analysis of Euclidean algorithms for polynomials over finite fields, J. Symb. Comput., 9, 429, 10.1016/S0747-7171(08)80021-1 Mayer, 1990, On the thermodynamic formalism for the Gauss map, Commun. Math. Phys., 130, 311, 10.1007/BF02473355 Roux, 2011 Ruelle, 2004 Schönhage, 1971, Schnelle Berechnung von Kettenbruchentwicklungen, Acta Inform., 1, 139, 10.1007/BF00289520 Schweiger, 2000, Multidimensional Continued Fractions Stehlé, 2004, A binary recursive gcd algorithm, vol. 3076, 411 Tenenbaum, 1990 Vallée, 2006, Euclidean dynamics, Discrete Contin. Dyn. Syst., 1, 281, 10.3934/dcds.2006.15.281 von zur Gathen, 2003 von zur Gathen, 2006, GCD of random linear combinations, Algorithmica, 46, 137, 10.1007/s00453-006-0072-1