Numerical Properties of the LLL Algorithm

The LLL algorithm is widely used to solve the integer least squares problems that arise in many engineering applications. As most practitioners did not understand how the LLL algorithm works, they avoided the issue by referring to the method as an integer Gram Schmidt approach (without explaining what they mean by this term). Luk and Tracy 1 were first to describe the behavior of the LLL algorithm, and they presented a new numerical implementation that should be more robust than the original LLL scheme. In this paper, we compare the numerical properties of the two different LLL implementations