In this paper, an extension of Kaczmarz method, the Kaczmarz method with oblique projection (KO), is introduced and analyzed. Using this method, a number of iteration steps to solve the over-determined systems of linear equations are significantly reduced, and the the computing time is much saved, especially for those problems that contain some linear equations with near-linear correlation. Simultaneously, a randomized version--randomized Kaczmarz method with oblique projection (RKO) is established. The convergence proofs of these two methods are given and numerical experiments show the effectiveness of the two methods for uniformly distributed random data. Especially when the system has correlated rows, the improvement of experimental results is very prominent.

翻译：本文介绍并分析了Kaczmarz法的延伸,即卡茨马尔兹法与斜投投法(KO)的延伸。使用这种方法,许多解决线性方程式定值过高系统的迭代步骤大大减少,计算时间节省了很多时间,特别是对于含有具有近线性相关性的线性方程的问题。同时,还建立了带有斜投法(RKO)的随机版-经调整的卡茨马尔兹法。提供了这两种方法的趋同证据,数字实验显示了统一分布随机数据的两种方法的有效性。特别是当系统有相关行时,实验结果的改进非常显著。