论文标题
线性系统的Kaczmarz-Tanabe方法的收敛速率
Convergence rates of the Kaczmarz-Tanabe method for linear systems
论文作者
论文摘要
在本文中，我们研究了Kaczmarz-Tanabe方法，以确切和不精确的线性系统。 kaczmarz-tanabe方法源自kaczmarz方法，但比这更稳定。 We analyze the convergence and the convergence rate of the Kaczmarz-Tanabe method based on the singular value decomposition theory, and discover two important factors, i.e., the second maximum singular value of $Q$ and the minimum non-zero singular value of $A$, that influence the convergence speed and the amplitude of fluctuation of the Kaczmarz-Tanabe method (even for the Kaczmarz method).数值测试验证了Kaczmarz-Tanabe方法的理论结果。
In this paper, we investigate the Kaczmarz-Tanabe method for exact and inexact linear systems. The Kaczmarz-Tanabe method is derived from the Kaczmarz method, but is more stable than that. We analyze the convergence and the convergence rate of the Kaczmarz-Tanabe method based on the singular value decomposition theory, and discover two important factors, i.e., the second maximum singular value of $Q$ and the minimum non-zero singular value of $A$, that influence the convergence speed and the amplitude of fluctuation of the Kaczmarz-Tanabe method (even for the Kaczmarz method). Numerical tests verify the theoretical results of the Kaczmarz-Tanabe method.
