LLL Algorithm: Analysis And Application

When solving the integer least squares problems arise in many engineering appli-cations, the LLL algorithm is widely used as a precondition. But the way how LLL algorithm works was seldom understood by the practitioners, until Luk and Tracy [11] first describe the behavior of the algorithm, and they also derive a new numerical im-plementation of LLL algorithm. Luk and Qiao [12] compare the origin and new LLL algorithms in the cases of overflow and underflow. In this paper, we first looked into the difference of the two implementations when they were applied to solve integer least squares problems. And then, we set a precondition for matrix to enhance the efficiency of LLL algorithm. After that, we would investigate into the effect of different values of the parameter in LLL algorithm. Meanwhile, we try to integrate QR decomposition with LLL algorithm.