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arXiv · 2212.06358

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

Nian-Ci Wu·Qian Zuo·Yatian Wang
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Abstract

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.

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Nian-Ci Wu, Qian Zuo, Yatian Wang. 2022-12-13. On the Polyak momentum variants of the greedy deterministic single and multiple row-action methods. https://doi.org/10.1002/nla.2552

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