An improved LLL algorithm

Luk FT; Tracy DA

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An improved LLL algorithm

机译：改进的LLL算法

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摘要

The LLL algorithm has received a lot of attention as an effective numerical tool for preconditioning an integer least squares problem. However, the workings of the algorithm are not well understood. In this paper, we present a new way to look at the LLL reduction, which leads to a new implementation method that performs better than the original LLL scheme. (c) 2007 Elsevier Inc. All rights reserved.

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《Linear Algebra and its Applications》 |2008年第3期|共12页
作者
Luk FT; Tracy DA;
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正文语种 eng
中图分类数理逻辑、数学基础;
关键词
LLL algorithm; integer least squares; unimodular transformation; reduced basis; Gauss transformation; QR decomposition; plane reflection; condition number; COMPLEXITY;

机译：LLL算法;整数最小二乘;单模变换;归约基;高斯变换;QR分解;平面反射;条件数;复杂度;

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机译：ISAbelle / HOL中的LLL基础减少算法和LLL分解算法
2. Commutative Algorithms Approximate the LLL-distribution [J] . Fotis Iliopoulos LIPIcs : Leibniz International Proceedings in Informatics . 2018,第1期

机译：交换算法近似的LLL分布
3. Boosted KZ and LLL Algorithms [J] . Shanxiang Lyu, Cong Ling IEEE Transactions on Signal Processing . 2017,第18期

机译：增强型KZ和LLL算法
4. Improving the Parallel Schnorr-Euchner LLL Algorithm [C] . Werner Backes, Susanne Wetzel ICA3PP 2011;International conference on algorithms and architectures for parallel processing . 2011

机译：改进并行Schnorr-Euchner LLL算法
5. Modified LLL algorithms [D] . Zhou, Tianyang 2006

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7. Formalizing the LLL Basis Reduction Algorithm and the LLL Factorization Algorithm in Isabelle/HOL [O] . René Thiemann, Ralph Bottesch, Jose Divasón, 2020

机译：ISAbelle / HOL中的LLL基础减少算法和LLL分解算法
8. Support the Design of Improved IUE NEWSIPS High Dispersion Extraction Algorithms: Improved IUE High Dispersion Extraction Algorithms [R] . Lawton, P. 2004

机译：支持改进的IUE NEWsIps高色散提取算法的设计：改进的IUE高色散提取算法

An improved LLL algorithm

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