A Block Chaotic and Asynchronous Algorithm for Consistent Systems with Incomplete Data (Journal of Computational Mathematics, 1993)
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 $$x_{i+r_i}=α_{j_i}x_{i+r_i-1}+(1-α_{j_i})P_{j_i,x_i}x_i$$ where $P_{j_i,x_i}, j=1,…,n$, are paracontracting and/or pseudocontracting matrices is analyzed. These iterations can also be applied to solve consistent systems with incomplete data.