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Designing linear distributed algorithms with memory for fast convergence
Author(s) -
Roy Sandip,
Wan Yan,
Saberi Ali,
Xue Mengran
Publication year - 2012
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1778
Subject(s) - invertible matrix , convergence (economics) , computer science , distributed memory , computation , algorithm , distributed algorithm , linear system , parallel computing , distributed computing , shared memory , mathematics , mathematical analysis , pure mathematics , economics , economic growth
SUMMARY 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.