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• W2048184489 abstract "In this paper, we provide polynomial bounds on the worst case bit-complexity of two formulations of the continued fraction algorithm. In particular, for a square-free integer polynomial of degree n with coefficients of bit-length L, we show that the bit-complexity of Akritas’ formulation is O˜(n8L3), and the bit-complexity of a formulation by Akritas and Strzeboński is O˜(n7L2); here O˜ indicates that we are omitting logarithmic factors. The analyses use a bound by Hong to compute the floor of the smallest positive root of a polynomial, which is a crucial step in the continued fraction algorithm. We also propose a modification of the latter formulation that achieves a bit-complexity of O˜(n5L2)." @default.
• W2048184489 created "2016-06-24" @default.
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• W2048184489 date "2008-12-01" @default.
• W2048184489 modified "2023-10-17" @default.
• W2048184489 title "Complexity of real root isolation using continued fractions" @default.
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• W2048184489 doi "https://doi.org/10.1016/j.tcs.2008.09.017" @default.
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