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Universal bounds for fixed point iterations via optimal transport metrics
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
-
Abstract
- 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.
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....1d7dfa1345b02b47e9836a2f22928253
- Full Text :
- https://doi.org/10.48550/arxiv.2108.00300