论文标题
在贪婪确定性单行方法和多个行动方法的polyak动量变体上
On the Polyak momentum variants of the greedy deterministic single and multiple row-action methods
论文作者
论文摘要
为了求解一致的线性方程系统，经典的行动（也称为kaczmarz）方法是一种简单的，而真正有效的迭代求解器。基于贪婪的指数选择策略和Polyak的重球动量加速技术，我们提出了两种确定性的行动方法，并建立了相应的收敛理论。我们表明，我们的算法可以线性收敛到最小二乘解决方案，并具有最小的欧几里得规范。已经提出了几项数值研究，以证实我们的理论发现。还出于说明目的，也提出了现实世界中的应用程序，例如计算机辅助几何设计中的数据拟合。
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.
