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

On multi-step extended maximum residual Kaczmarz method for solving large inconsistent linear systems