Local Linear Convergence of Alternating Projections in Metric Spaces with Bounded Curvature
研究了交替投影法在度量空间中寻找两个闭集交点的局部线性收敛性，通过测地线和角度（Alexandrov意义）揭示了收敛所需的两个几何条件：横截性条件和均匀测地逼近条件。
We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, equipped only with well-behaved geodesics and angles (in the sense of Alexandrov), we are able to highlight the two key geometric ingredients in a standard intuitive analysis of local linear convergence. The first is a transversality-like condition on the intersection; the second is a convexity-like condition on one set: “uniform approximation by geodesics."