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»ã±¨¼ò½é£º Lattice basis reduction has a wide range of applications, such as mathematics, cryptography, wireless communication, and GPS, just to name a few. There are several notions of basis reduction. We propose a completely new approach to lattice reduction: Jacobi-type methods. A Jacobi method has a two dimensional workhorse. In the case of symmetric eigenvalue problem, the workhorse is the two dimensional symmetric eigenvalue decomposition. In our case, the workhorse is the Lagrange algorithm for two dimensional lattice reduction. While the basic idea behind our Jacobi-type methods is simple, the challenge is to prove its convergence and analyze its computational complexity. Jacobi method is attractive, because it is inherently parallel. In this talk, after introducing the background, we present our recent results on the Jacobi-type methods for lattice reduction, including the generic method, the modified methods, the convergence, the computational complexity, a parallel algorithm and its GPU implementation.

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