Algorithmic (Semi-)Conjugacy via Koopman Operator Theory
Data Structures and Algorithms
2022-09-15 v1 Dynamical Systems
Abstract
Iterative algorithms are of utmost importance in decision and control. With an ever growing number of algorithms being developed, distributed, and proprietarized, there is a similarly growing need for methods that can provide classification and comparison. By viewing iterative algorithms as discrete-time dynamical systems, we leverage Koopman operator theory to identify (semi-)conjugacies between algorithms using their spectral properties. This provides a general framework with which to classify and compare algorithms.
Cite
@article{arxiv.2209.06374,
title = {Algorithmic (Semi-)Conjugacy via Koopman Operator Theory},
author = {William T. Redman and Maria Fonoberova and Ryan Mohr and Ioannis G. Kevrekidis and Igor Mezić},
journal= {arXiv preprint arXiv:2209.06374},
year = {2022}
}
Comments
6 pages, 5 figures, accepted to IEEE CDC 2022