On the Polyak momentum variants of the greedy deterministic single and multiple row-action methods

For solving a consistent system of linear equations, the classical row-action (also known as Kaczmarz) method is a simple while really effective iteration solver. Based on the greedy index selection strategy and Polyak's heavy-ball momentum acceleration technique, we propose two deterministic r...

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Bibliographic Details
Published in:arXiv.org 2022-12
Main Authors: Wu, Nian-Ci, Zuo, Qian, Wang, Yatian
Format: Article
Language:English
Subjects:
Algorithms
CAD
Computer aided design
Convergence
Iterative methods
Linear equations
Momentum
Online Access:Get full text
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Summary:For solving a consistent system of linear equations, the classical row-action (also known as Kaczmarz) method is a simple while really effective iteration solver. Based on the greedy index selection strategy and Polyak's heavy-ball momentum acceleration technique, we propose two deterministic row-action methods and establish the corresponding convergence theory. We show that our algorithm can linearly converge to a least-squares solution with minimum Euclidean norm. Several numerical studies have been presented to corroborate our theoretical findings. Real-world applications, such as data fitting in computer-aided geometry design, are also presented for illustrative purposes.
ISSN:2331-8422
DOI:10.48550/arxiv.2212.06358