A Block Chaotic and Asynchronous Algorithm for Consistent Systems with Incomplete Data

Abstract

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 $P_{j_i,x_i}, j=1,\cdots,n$, are paracontracting and/or pseudocontracting matrices is analyzed. These iterations can also be applied to solve consistent systems with incomplete data.