Designing linear distributed algorithms with memory for fast convergence

Motivated by both distributed computation and decentralized control applications, we studied the distributed linear iterative algorithms with memory. Specifically, we showed that the system of linear equations G x = b can be solved through a distributed linear iteration for arbitrary invertible G using only a single memory element at each processor. Further, we demonstrated that the memoried distributed algorithm can be designed to achieve much faster convergence than a memoryless distributed algorithm. Two small simulation examples were included to illustrate the results. Copyright © 2011 John Wiley & Sons, Ltd.