A Probabilistic, -euclidean Althorthm That Yielps Small Coefficients
نویسندگان
چکیده
Given n positive integers a 1.a2• ••• .a,... a probabilistic algorithm for the solution of the equation 1& • 'LajXj=gcd(al.a2.· .• .a,..) is provided. The algorithm has the.following properties: If the distribution j=f of the aj's over an interval [O,2t+l) is uniform or nonincreasing and the density of the aj's n log9/s(k+lie) d I ( ) satisfies the inequality d~l+ k ' then the algorithm succeeds with probilbilog maxaj , ity greater than l-e and the resulting x;'s satisfy the inequalities: max IXj I<O.62(maxaj )0.694 and LlxjJ <1.004(ntaxaj)O.694. A more general problem is solved in a similar way. T ec hn io n C om pu te r Sc ie nc e D ep ar tm en t T eh ni ca l R ep or t C S0 48 1 19 87
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