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In this paper, we generalize the paracontracting matrices to pseudocontracting matrices. The convergence of (parallel) iteration x_i=P_ji,x_i-1 x_i-1 and x_i+r_i=α_j_ix_i+r_i-1+(1-α_j_i)P_j_i,x_ix_i where P_j_i,x_i