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Unifying Random-Asynchronous Algorithms for Numerical Methods, Using Switching Systems Theory

Teke, Oguzhan and Vaidyanathan, P. P. (2021) Unifying Random-Asynchronous Algorithms for Numerical Methods, Using Switching Systems Theory. In: 2021 55th Asilomar Conference on Signals, Systems, and Computers. IEEE , Piscataway, NJ, pp. 172-176. ISBN 978-1-6654-5828-3. https://resolver.caltech.edu/CaltechAUTHORS:20220317-376196000

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Abstract

Randomized variants of iterative techniques such as Kaczmarz method, Gauss-Seidel method and asynchronous fixed-point iterations have been of interest in recent years. Due to their randomized nature, these techniques are better suited for processing of large scale and distributed data. Despite their effectiveness, their theoretical analysis has been of interest only in recent years. In the mean-time, control theory literature has studied switching systems rigorously in order to understand the behavior of systems whose dynamics change over time. This paper shows that randomized iterative algorithms can be represented as switching systems. Thus, convergence properties of such randomized algorithms follow directly from the stability theory already developed for switching systems. As an example, alternative proofs are provided for the mean-squared and almost sure convergence of randomized Kaczmarz and Gauss-Seidel methods. The necessary and sufficient condition for the mean-squared convergence of random asynchronous fixed-point iterations is also provided.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/IEEECONF53345.2021.9723385DOIArticle
ORCID:
AuthorORCID
Teke, Oguzhan0000-0002-1131-5206
Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© 2021 IEEE. This work was supported by the Office of Naval Research grant N00014-21-1-2521, and the California Institute of Technology
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-21-1-2521
CaltechUNSPECIFIED
DOI:10.1109/ieeeconf53345.2021.9723385
Record Number:CaltechAUTHORS:20220317-376196000
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220317-376196000
Official Citation:O. Teke and P. P. Vaidyanathan, "Unifying Random-Asynchronous Algorithms for Numerical Methods, Using Switching Systems Theory," 2021 55th Asilomar Conference on Signals, Systems, and Computers, 2021, pp. 172-176, doi: 10.1109/IEEECONF53345.2021.9723385
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:113937
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:18 Mar 2022 21:12
Last Modified:18 Mar 2022 21:12

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