Effect of the interval-symbol method with correct zero rewriting on the δ-LLL algorithm

We previously proposed the interval-symbol method with correct zero rewriting (ISCZ method) to reduce the amount of exact computations to obtain the exact results by aid of floating-point computations. Recently we have presented new ideas for reducing time and memory of executing the ISCZ method. In...

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Published in:ACM communications in computer algebra 2018-06, Vol.52 (2), p.24-31
Main Authors: Nagashima, Hiroki, Shirayanagi, Kiyoshi
Format: Article
Language:English
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Summary:We previously proposed the interval-symbol method with correct zero rewriting (ISCZ method) to reduce the amount of exact computations to obtain the exact results by aid of floating-point computations. Recently we have presented new ideas for reducing time and memory of executing the ISCZ method. In this paper, we apply the new ISCZ method to the δ-LLL algorithm, which is a generalization of the Lenstra-Lenstra-Lovász (LLL) lattice reduction algorithm. By Maple experiments, we confirm its superiority over the original ISCZ method, and in the irrational case we show its great effect on the δ-LLL algorithm in the sense that it is much more efficient than the purely exact approach.
ISSN:1932-2240
DOI:10.1145/3282678.3282679