# On local convergence of the method of alternating projections

arXiv: https://arxiv.org/abs/1312.5681 · HTML: https://mlsanity.com/paper/1312.5681/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2013.

## Built on by (most cited first, 2 of 2)

- [Provable Phase Retrieval with Mirror Descent](https://mlsanity.com/paper/2210.09248/) (2022)
- [Optimization over the intersection of manifolds](https://mlsanity.com/paper/2605.22736/) (2026)

## Abstract (arXiv)

The method of alternating projections is a classical tool to solve feasibility problems. Here we prove local convergence of alternating projections between subanalytic sets A,B under a mild regularity hypothesis on one of the sets. We show that the speed of convergence is O(k-ρ) for some ρ∈ (0,∞).