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

Wu, Nian‐Ci; Zuo, Qian; Wang, Yatian

For solving a consistent system of linear equations, the classical row‐action method, such 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.

LINEAR equations; LINEAR systems; COMPUTER-aided design

Numerical Linear Algebra with Applications, 2024, Vol 31, Issue 4, p1

1070-5325

Academic Journal

10.1002/nla.2552