标题： 通过最优传输度量的固定点迭代的通用界限 显示英文标题

标题： Universal bounds for fixed point iterations via optimal transport metrics

摘要： 我们对非负整数集合上的特定度量族进行了自包含的分析。 我们证明，这些度量通过嵌套序列的最优传输问题定义，为非扩张映射的一般Krasnosel'skii-Mann不动点迭代提供了紧密估计。 我们还描述了它们的一些非常特殊的性质，包括单调性和所谓的“凸四边形不等式”，该不等式可用来高效计算它们的贪心算法。 显示英文摘要

摘要： We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for general Krasnosel'skii-Mann fixed point iterations for non-expansive maps. We also describe some of their very special properties, including their monotonicity and the so-called "convex quadrangle inequality" that yields a greedy algorithm to compute them efficiently.