# Fast Krasnoselskii-Mann Method with Overrelaxation and Preconditioners

arXiv: https://arxiv.org/abs/2411.18574 · HTML: https://mlsanity.com/paper/2411.18574/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2024.

## Built on by (most cited first, 1 of 1)

- [Stochastic Inertial Krasnosel'skii-Mann Iteration Achieves Near-Optimal Sample Complexity](https://mlsanity.com/paper/2609.28543/) (2026)

## Abstract (arXiv)

We study accelerated Krasnoselskii-Mann-type methods with preconditioners in both continuous and discrete time. From a continuous-time model, we derive a generalized fast Krasnoselskii-Mann method, providing a new yet simple proof of convergence that leads to unprecedented flexibility in parameter tuning, allowing up to twice larger relaxation parameters. Our analysis unifies inertial and anchoring acceleration mechanisms and offers a broad range of parameter choices, which prove beneficial in practice. Additionally, we extend our analysis to the case where preconditioners are allowed to be degenerate, unifying the treatment of various splitting methods and establishing the weak convergence of shadow sequences.