### 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) |
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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 |

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

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## Cite this

Liu, J., Morse, A. S., Nedic, A., & Basar, T. (2014). Stability of a distributed algorithm for solving linear algebraic equations.

*Proceedings of the IEEE Conference on Decision and Control*,*2015-February*(February), 3707-3712. [7039966]. https://doi.org/10.1109/CDC.2014.7039966