论文标题
用于计算动态系统适应指标的预测亚级别方法
A Projected Subgradient Method for the Computation of Adapted Metrics for Dynamical Systems
论文作者
论文摘要
在本文中，我们扩展了一种最近建立的亚级别方法，用于计算Riemannian指标，以优化与动态系统相关的某些奇异值函数。此扩展是三倍。首先，我们引入了一种投影的亚级别方法，该方法导致了Riemannian指标，其参数仅限于紧凑型凸集，因此我们可以证明存在最小化器；其次，我们允许不精确的亚级别并研究误差对计算指标的影响。第三，我们分析了三种不同选择的阶梯尺寸选择：恒定，外源性和polyak。新方法通过应用于Hénon地图的维度和熵估计来说明。
In this paper, we extend a recently established subgradient method for the computation of Riemannian metrics that optimizes certain singular value functions associated with dynamical systems. This extension is threefold. First, we introduce a projected subgradient method which results in Riemannian metrics whose parameters are confined to a compact convex set and we can thus prove that a minimizer exists; second, we allow inexact subgradients and study the effect of the errors on the computed metrics; and third, we analyze the subgradient algorithm for three different choices of step sizes: constant, exogenous and Polyak. The new methods are illustrated by application to dimension and entropy estimation of the Hénon map.
