Formalizing the LLL Basis Reduction Algorithm and the LLL Factorization Algorithm in Isabelle/HOL

An improved LLL algorithm

6 The LLL algorithm has received a lot of attention as an effective numerical tool for preconditioning 7 an integer least squares problem. However, the workings of the algorithm are not well understood. In this 8 paper, we present a new way to look at the LLL reduction, which leads to a new implementation method 9 that performs better than the original LLL scheme. 10 © 2007 Published by Elsevie...

The History of the LLL-Algorithm

The LLL Algorithm - Survey and Applications

Bargaining with reading habit is no need. Reading is not kind of something sold that you can take or not. It is a thing that will change your life to life better. It is the thing that will give you many things around the world and this universe, in the real world and here after. As what will be given by this the lll algorithm survey and applications, how can you bargain with the thing that has ...

Conditioning Properties of the LLL Algorithm

Although the LLL algorithm was originally developed for lattice basis reduction, the method can also be used to reduce the condition number of a matrix. In this paper, we propose a pivoted LLL algorithm that further improves the conditioning. Our experimental results demonstrate that this pivoting scheme works well in practice.

SIMULTANEOUS RATIONAL APPROXIMATIONS OF p-ADIC NUMBERS BY THE LLL LATTICE BASIS REDUCTION ALGORITHM

In this paper we construct multi-dimensional p-adic approximation lattices by simultaneous rational approximations of p-adic numbers. For analyzing these p-adic lattices we apply the LLL algorithm due to Lenstra, Lenstra and Lovász, which has been widely used to solve the various NP problems such as SVP (Shortest Vector Problems), ILP (Integer Linear Programing) .. and so on. In a twodimensiona...