# Convergence rate analysis for averaged fixed point iterations in the presence of H"older regularity

arXiv: https://arxiv.org/abs/1510.06823 · HTML: https://mlsanity.com/paper/1510.06823/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2015.

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

- [Trilevel and Multilevel Optimization using Monotone Operator Theory](https://mlsanity.com/paper/2105.09407/) (2021)
- [Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems](https://mlsanity.com/paper/2606.18305/) (2026)

## Abstract (arXiv)

In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded H"older regularity assumption which generalizes the well-known notion of bounded linear regularity. As an application of our results, we provide a convergence rate analysis for Krasnoselskii-Mann iterations, the cyclic projection algorithm, and the Douglas-Rachford feasibility algorithm along with some variants. In the important case in which the underlying sets are convex sets described by convex polynomials in a finite dimensional space, we show that the H"older regularity properties are automatically satisfied, from which sublinear convergence follows.