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A Note On Convergence Rate of Randomized Kaczmarz Method
Calcolo ( IF 1.7 ) Pub Date : 2020-08-08 , DOI: 10.1007/s10092-020-00376-4
Ying-Jun Guan , Wei-Guo Li , Li-Li Xing , Tian-Tian Qiao

In this paper, we propose an alternative version of the randomized Kaczmarz method, which chooses each row of the coefficient matrix A with probability proportional to the square of the Euclidean norm of the residual of each corresponding equation. We prove that it converges with expected linear rate and the convergence rate of this method is better than the Strohmer and Vershynin’s RK method. Numerical experiments also show this method is more efficient than the RK method.

中文翻译:

随机Kaczmarz方法收敛速度的一个注记。

在本文中,我们提出了另一种形式的随机Kaczmarz方法,该方法选择系数矩阵A的每一行,其概率与每个相应方程的残差的欧几里得范数的平方成正比。我们证明了它与期望的线性速率收敛,并且该方法的收敛速率优于Strohmer和Vershynin的RK方法。数值实验还表明,该方法比RK方法更有效。
更新日期:2020-08-08
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