A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is convergent and gives an upper bound on its convergence rate. Numerical experiments show that the proposed method is effective and outperforms the existing extended Kaczmarz methods in terms of the number of iteration steps and the computational costs.

翻译：本文提出了一种多步扩展最大残差Kaczmarz方法，通过采用多步迭代技术求解大型不相容线性方程组。理论分析证明了所提方法的收敛性，并给出了其收敛速率的上界。数值实验表明，所提方法有效且在迭代步数和计算成本方面优于现有的扩展Kaczmarz方法。