利用交错投影构造Grassmannian流形中的填充
Constructing packings in Grassmannian manifolds via alternating projection
摘要：
本文描述了一种寻找具有各种度量的格拉斯曼流形中的良好填充的数值方法。这项研究也包括包装在射影空间。在每一种情况下，产生一个好的填充等价于构造一个具有一定结构和谱性质的矩阵。通过交替地实施结构条件和谱条件，通常可以得到满足两者的矩阵。然后可以从该矩阵中提取填料。这种方法既强大又通用。在已经进行实验的情况下，交替投影方法产生的填充与记录的最佳填充竞争。它还延伸到没有被数值研究的问题。例如，它可以用来产生包装的子空间在真正的和复杂的格拉斯曼空间配备了富比尼-研究距离;这些包装是有价值的无线通信。人们可以证明，一些新的配置构造的算法具有包装直径是接近最佳的。
英文摘要：
This paper describes a numerical method for finding good packings in Grassmannian manifolds equipped with various metrics. This investigation also encompasses packing in projective spaces. In each case, producing a good packing is equivalent to constructing a matrix that has certain structural and spectral properties. By alternately enforcing the structural condition and then the spectral condition, it is often possible to reach a matrix that satisfies both. One may then extract a packing from this matrix. This approach is both powerful and versatile. In cases where experiments have been performed, the alternating projection method yields packings that compete with the best packings recorded. It also extends to problems that have not been studied numerically. For example, it can be used to produce packings of subspaces in real and complex Grassmannian spaces equipped with the Fubini--Study distance; these packings are valuable in wireless communications. One can prove that some of the novel configurations constructed by the algorithm have packing diameters that are nearly optimal.
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