Conditioning properties of the LLL algorithm
Franklin T. Luk, Sanzheng Qiao · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
Although the LLL algorithm1 was originally developed for lattice basis reduction, the method can also be used2 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.