For solving large-scale consistent linear system, we combine two efficient row index selection strategies with Kaczmarz-type method with oblique projection, and propose a greedy randomized Kaczmarz method with oblique projection (GRKO) and the maximal weighted residual Kaczmarz method with oblique projection (MWRKO) . Through those method, the number of iteration steps and running time can be reduced to a greater extent to find the least-norm solution, especially when the rows of matrix A are close to linear correlation. Theoretical proof and numerical results show that GRKO method and MWRKO method are more effective than greedy randomized Kaczmarz method and maximal weighted residual Kaczmarz method respectively.

翻译：为了解决大规模一致线性系统问题,我们将两个高效的行指数选择战略与卡兹马尔兹型方法与斜线投影相结合,并提议一种贪婪的随机卡兹马尔兹法,采用斜线投影法和最大加权剩余卡兹马尔兹法,采用斜线投影法。通过这种方法,迭代步骤和运行时间可以更大幅度地减少,以找到最不中性的解决办法,特别是当矩阵A的行接近线性相关时。理论证据和数字结果显示,GRKO法和MWRKO法分别比贪婪的随机卡兹马尔兹法和最高加权剩余卡茨马尔兹法更有效。