  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.
