论文标题
关于Chebyshev Norm中矩阵的最佳级别1近似
On the optimal rank-1 approximation of matrices in the Chebyshev norm
论文作者
论文摘要
低级近似的问题在科学中无处不在。传统上，由于存在有效的构建近似方法，因此以统一的不变规范（例如Frobenius或光谱规范）解决了这个问题。但是，最近的结果揭示了Chebyshev Norm中低级近似值的潜力，Chebyshev Norm自然而然地出现了许多应用。在本文中，我们解决了在Chebyshev Norm中构建最佳排名1近似值的问题。我们研究了用于构建低级近似值的交替最小化算法的特性，并演示了如何使用它来构建最佳秩-1近似。结果，我们提出了一种算法，该算法能够在小矩阵中构建Chebyshev Norm中的最佳级别1近似值。
The problem of low rank approximation is ubiquitous in science. Traditionally this problem is solved in unitary invariant norms such as Frobenius or spectral norm due to existence of efficient methods for building approximations. However, recent results reveal the potential of low rank approximations in Chebyshev norm, which naturally arises in many applications. In this paper we tackle the problem of building optimal rank-1 approximations in the Chebyshev norm. We investigate the properties of alternating minimization algorithm for building the low rank approximations and demonstrate how to use it to construct optimal rank-1 approximation. As a result we propose an algorithm that is capable of building optimal rank-1 approximations in Chebyshev norm for small matrices.
