The Lattice Reduction Algorithm of Gauss: An Average Case Analysis
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چکیده
The lattice reduction algorithm of Gauss is shown to have an average case complexity which is asymptotic to a constant. Introduction. The “reduction” algorithm of Gauss plays an important r6le in several areas of computational number theory, principally in matters related to the reduction of integer lattice bases. It is also intimately connected with extensions to complex numbers of the Euclidean gcd algorithms and continued fraction expansions. Continued Fractions. Every rational or real number has a continued fraction expansion. For instance, the number 193/71 w 2.71830 leads to 1 E = 2 + 1 , (1) 1+ 71 1
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تاریخ انتشار 1990