Abstract
In [1], given a matrix A and a vector b, a distributed algorithm was proposed for solving linear algebraic equations of the form Ax = b when there is at least one solution. The equation is simultaneously solved by a group of autonomous agents whose neighbor relations are characterized by a time-dependent directed graph. The main contribution of this paper is to provide necessary and sufficient conditions for exponential convergence of the algorithm under the most general assumption. These conditions utilize a new notion of graph connectivity which is less restrictive than strong connectivity.
| Original language | English (US) |
|---|---|
| Article number | 7039966 |
| Pages (from-to) | 3707-3712 |
| Number of pages | 6 |
| Journal | Proceedings of the IEEE Conference on Decision and Control |
| Volume | 2015-February |
| Issue number | February |
| DOIs | |
| State | Published - Jan 1 2014 |
| Event | 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: Dec 15 2014 → Dec 17 2014 |
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ASJC Scopus subject areas
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization
Cite this
Stability of a distributed algorithm for solving linear algebraic equations. / Liu, Ji; Morse, A. Stephen; Nedic, Angelia; Basar, Tamer.
In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2015-February, No. February, 7039966, 01.01.2014, p. 3707-3712.Research output: Contribution to journal › Conference article
}
TY - JOUR
T1 - Stability of a distributed algorithm for solving linear algebraic equations
AU - Liu, Ji
AU - Morse, A. Stephen
AU - Nedic, Angelia
AU - Basar, Tamer
PY - 2014/1/1
Y1 - 2014/1/1
N2 - In [1], given a matrix A and a vector b, a distributed algorithm was proposed for solving linear algebraic equations of the form Ax = b when there is at least one solution. The equation is simultaneously solved by a group of autonomous agents whose neighbor relations are characterized by a time-dependent directed graph. The main contribution of this paper is to provide necessary and sufficient conditions for exponential convergence of the algorithm under the most general assumption. These conditions utilize a new notion of graph connectivity which is less restrictive than strong connectivity.
AB - In [1], given a matrix A and a vector b, a distributed algorithm was proposed for solving linear algebraic equations of the form Ax = b when there is at least one solution. The equation is simultaneously solved by a group of autonomous agents whose neighbor relations are characterized by a time-dependent directed graph. The main contribution of this paper is to provide necessary and sufficient conditions for exponential convergence of the algorithm under the most general assumption. These conditions utilize a new notion of graph connectivity which is less restrictive than strong connectivity.
UR - http://www.scopus.com/inward/record.url?scp=84988289973&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84988289973&partnerID=8YFLogxK
U2 - 10.1109/CDC.2014.7039966
DO - 10.1109/CDC.2014.7039966
M3 - Conference article
AN - SCOPUS:84988289973
VL - 2015-February
SP - 3707
EP - 3712
JO - Proceedings of the IEEE Conference on Decision and Control
JF - Proceedings of the IEEE Conference on Decision and Control
SN - 0191-2216
IS - February
M1 - 7039966
ER -