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.

翻译：在本文中,我们调查了卡兹马尔兹-塔纳贝法对精确和不精确线性系统的作用。卡兹马尔兹-塔纳贝法来自卡兹马尔兹法,但比这更稳定。我们根据单值分解理论分析了卡兹马尔兹-塔纳贝法的趋同率和趋同率,并发现了两个重要因素,即美元第二最大单值和美元最低非零单值,这影响到卡兹马尔兹-塔纳贝法(甚至卡兹马尔兹法)的趋同速度和波动幅度。数字测试证实了卡兹马尔兹-塔纳贝法的理论结果。