论文标题
汉克尔结构的低级近似的梯度系统方法
A gradient system approach for Hankel structured low-rank approximation
论文作者
论文摘要
排名不足的Hankel矩阵是几种应用程序的核心。但是，实际上，由于例如，这些矩阵的系数嘈杂。测量误差和计算错误，因此相关矩阵通常是全等级。这激发了Hankel结构的低级近似问题。总体而言，结构化的低级近似问题没有全球和有效的解决方案技术。在本文中，我们提出了一种基于两级迭代的局部优化方法。实验结果表明，与替代方法相比，所提出的算法通常可以达到良好的准确性，并且相对于初始近似值表现出更高的鲁棒性。
Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are full rank. This motivates the problem of Hankel structured low-rank approximation. Structured low-rank approximation problems, in general, do not have a global and efficient solution technique. In this paper we propose a local optimization approach based on a two-levels iteration. Experimental results show that the proposed algorithm usually achieves good accuracy and shows a higher robustness with respect to the initial approximation, compared to alternative approaches.
