PAPERZILLA
Crunching Academic Papers into Bite-sized Insights.
About
Sign Out
← Back to papers

Physical SciencesMathematicsNumerical Analysis

Exact Optimal Accelerated Complexity for Fixed-Point Iterations

SHARE

Overview

Paper Summary
Conflicts of Interest
Identified Weaknesses
Rating Explanation
Good to know
Topic Hierarchy
File Information

Paper Summary

Paperzilla title
A Faster Pendulum Swing: Optimizing Fixed-Point Iterations
This paper introduces an accelerated method and a matching complexity lower bound for fixed-point iterations, proving its optimality under specific conditions like nonexpansive and contractive operators. The acceleration also extends to some settings where the operator exhibits Hölder-type growth. Practical experiments demonstrate some effectiveness, though further research is needed to assess the real-world impact across different problem domains and suboptimality measures.

Possible Conflicts of Interest

None identified

Identified Weaknesses

Practical Impact Uncertainty
While theoretically interesting and potentially impactful on other algorithms, the real-world significance of this theoretical acceleration is uncertain, and requires further investigation with more complex practical problems and diverse evaluation metrics.
Parameter Tuning Difficulty
The dependence on unknown parameters for the restarted algorithm in practice necessitates potentially expensive grid searches to determine the optimal schedule, diminishing its overall practicality.

Rating Explanation

This paper presents a novel acceleration mechanism for fixed-point iterations with matching lower complexity bounds, establishing exact optimality in certain cases. While the practical impact requires further investigation, the theoretical contributions are significant and potentially impactful on a wide class of algorithms.

Good to know

This is our free standard analysis. Paperzilla Pro fact-checks every citation, researches author backgrounds and funding sources, and uses advanced AI reasoning for more thorough insights.
Explore Pro →

Topic Hierarchy

File Information

Original Title:
Exact Optimal Accelerated Complexity for Fixed-Point Iterations
File Name:
paper_554.pdf
[download]
File Size:
1.89 MB
Uploaded:
August 22, 2025 at 08:54 PM
Privacy:
🌐 Public
© 2025 Paperzilla. All rights reserved.

If you are not redirected automatically, click here.