Designing linear distributed algorithms with memory for fast convergence

Motivated by both distributed-computation and decentralized-control applications, we study distributed linear iterative algorithms with memory. Specifically, we show that the system of linear equations Gx = b can be solved through a distributed linear iteration for arbitrary invertible G, using only a single memory element at each processor. Further, we demonstrate that the memoried distributed algorithm can be designed to achieve much faster convergence than a memoryless distributed algorithm. A small simulation example is included to illustrate the results.