### Citations

532 | Randomized gossip algorithms
- Boyd, Ghosh, et al.
- 2006
(Show Context)
Citation Context ...e, our study is most closely connected to that of Cao (which builds on the earlier work of Boyd), in that memoried iterations are being used to achieve convergence and to improve the convergence rate =-=[5, 7]-=-. However, here, we consider explicit design of the algorithm weights for verifiable convergence and performance shaping, allow for a much more general interaction topology, and use a more general cla... |

468 | Gossip-based computation of aggregate information - Kempe, Dobra, et al. |

446 |
Iterative Methods for Solving Linear Systems
- GREENBAUM
- 1997
(Show Context)
Citation Context ...k-synchronization applications where the augmentation may be hardwired) and (ii) this update is desirable in many numerical procedures (see the classical work on iterative solutions of linear systems =-=[1, 4]-=- for justification). Second, we again stress that, in general, the processor may only have access to the statistic yi Œk and not to the particular internal statuses of any particular processor (inclu... |

224 | Gossip algorithms: design, analysis and applications - Boyd, Ghosh, et al. - 2005 |

177 |
Decentralized Control of Complex Systems
- Siljak
- 1991
(Show Context)
Citation Context ...nded memories at the processors [7]. Meanwhile, the problem of shaping network dynamics has, in parallel, been studied in the control engineering community, under the heading of decentralized control =-=[10]-=-. Unfortunately, the wide historical literature in decentralized control is not apt for distributed algorithm construction, because these works view the network as a disturbance to be dominated rather... |

133 | Tsitsiklis, “Convergence speed in distributed consensus and averaging
- Olshevsky, N
- 2011
(Show Context)
Citation Context ... the condition number rather than with the condition number itself. Some recent and classical works have shown, in limited cases, that non-memoried iterations cannot achieve this level of performance =-=[3, 21]-=-; thus, our work clearly indicates the benefit of memoried iterations over non-memoried ones. Copyright © 2011 John Wiley & Sons, Ltd. Int. J. Robust. Nonlinear Control 2012; 22:1691–1702 DOI: 10.1002... |

51 | Convex optimization of graph laplacian eigenvalues - Boyd - 2006 |

41 |
System Theory and
- Linear
- 1984
(Show Context)
Citation Context ... the first n entries in the vector aŒk (i.e., the vector xŒk) converge quickly to the vector G1b; hence, the system of linear equations is solved. From classical results on linear system stability =-=[17]-=- along with characterization of the fixed point of the dynamics (3), we immediately obtain the following implicit condition under which the iteration finds the solution to the system of equations. The... |

23 |
Formation and alignment of distributed sensing agents with double integrator dynamics,"
- Roy, Saberi, et al.
- 2004
(Show Context)
Citation Context ...stem (1) that would work for a broad class of nonsymmetric matrices G. Their result, which incidentally has been occasionally revisited in the decentralized controls and numerical methods communities =-=[18,19]-=-, can be phrased in purely linear algebraic terms as follows. Lemma 1 (Fisher and Fuller [2]) If an n n matrix G has a sequence of n nested principal minors (with dimensions 1 1, 2 2, : : : , n ... |

18 | Accelerated gossip algorithms for distributed computation
- Cao, Spielman, et al.
- 2006
(Show Context)
Citation Context ...er linear distributed algorithms (in particular, faster distributed consensus algorithms used in, for example, sensor-fusion applications) can be constructed using extended memories at the processors =-=[7]-=-. Meanwhile, the problem of shaping network dynamics has, in parallel, been studied in the control engineering community, under the heading of decentralized control [10]. Unfortunately, the wide histo... |

12 | Stoorvogel A. A multiple-derivative and multiple-delay paradigm for decentralized controller design: uniform rank systems
- Wan, Roy, et al.
(Show Context)
Citation Context ...VERGENCE 1697 Remark Although we have proved this lemma from the first principles here, it is deeply connected with the philosophy for decentralized controller design introduced in our recent studies =-=[12, 13]-=-. In these studies, we have put forth the idea that derivatives of local observations used in feedback can permit stabilization and pole placement in decentralized systems. It turns out that these der... |

12 |
A new focus in the science of networks: towards methods for design
- Wan, Roy, et al.
- 2008
(Show Context)
Citation Context ...] for the simple argument). Several recent studies have pursued optimization of the condition number through diagonal scaling for particular matrix classes (e.g., symmetric positive-definite matrices =-=[11, 15, 20]-=-). However, in general, condition numbers may remain large upon diagonal scaling, and the convergence rate for an iteration without memory will be large. Here, we will demonstrate that the memoried it... |

10 |
Scaling: a canonical design problem for networks
- Roy, Saberi
- 2007
(Show Context)
Citation Context ...] for the simple argument). Several recent studies have pursued optimization of the condition number through diagonal scaling for particular matrix classes (e.g., symmetric positive-definite matrices =-=[11, 15, 20]-=-). However, in general, condition numbers may remain large upon diagonal scaling, and the convergence rate for an iteration without memory will be large. Here, we will demonstrate that the memoried it... |

6 | A design for multi-lead-compensators for stabilization and pole placement in double-integrator networks
- Wan, Roy, et al.
(Show Context)
Citation Context ...VERGENCE 1697 Remark Although we have proved this lemma from the first principles here, it is deeply connected with the philosophy for decentralized controller design introduced in our recent studies =-=[12, 13]-=-. In these studies, we have put forth the idea that derivatives of local observations used in feedback can permit stabilization and pole placement in decentralized systems. It turns out that these der... |

6 |
Network Design Problems for Controlling Virus Spread,” in
- Wan, Roy, et al.
- 2007
(Show Context)
Citation Context ...] for the simple argument). Several recent studies have pursued optimization of the condition number through diagonal scaling for particular matrix classes (e.g., symmetric positive-definite matrices =-=[11, 15, 20]-=-). However, in general, condition numbers may remain large upon diagonal scaling, and the convergence rate for an iteration without memory will be large. Here, we will demonstrate that the memoried it... |

2 |
On the stabilization of matrices and the convergence of linear iterative processes
- ME, AT
- 1958
(Show Context)
Citation Context ...xt. We note that another classical iterative method, developed by Fisher and Fuller, implicitly enforces decentralization in analogy with our work but only considers a memoryless (one-term) iteration =-=[2]-=-. It is worth noting that we have focused here on the problem of solving linear systems, but the methodology can be adapted to other distributed Copyright © 2011 John Wiley & Sons, Ltd. Int. J. Robust... |

2 | A control-theoretic approach on distributed discrete-valued decision-making in networks of sensing agents - Roy, Herlugson, et al. |

2 | An explicit formula for difference between Laplacian-eigenvector components using coalesced graphs. Linear Algebra and its Applications 2010 - Wan, Roy |

1 |
A historical review of iterative methods
- DM
- 1987
(Show Context)
Citation Context ...k-synchronization applications where the augmentation may be hardwired) and (ii) this update is desirable in many numerical procedures (see the classical work on iterative solutions of linear systems =-=[1, 4]-=- for justification). Second, we again stress that, in general, the processor may only have access to the statistic yi Œk and not to the particular internal statuses of any particular processor (inclu... |

1 |
Second-degree iterative methods for the solution of large linear systems
- DM
- 1972
(Show Context)
Citation Context ...erical methods for solving large linear systems given in, for example, [2–4]. Our iterative method may be viewed as a generalization of the classical two-term stationary iteration introduced by Young =-=[3]-=-, with the generalization necessitated by the need for a distributed algorithm in our context. We note that another classical iterative method, developed by Fisher and Fuller, implicitly enforces dece... |

1 |
Stabilization with decentralized feedback control
- JP, AS
- 1976
(Show Context)
Citation Context ...stem (1) that would work for a broad class of nonsymmetric matrices G. Their result, which incidentally has been occasionally revisited in the decentralized controls and numerical methods communities =-=[18,19]-=-, can be phrased in purely linear algebraic terms as follows. Lemma 1 (Fisher and Fuller [2]) If an n n matrix G has a sequence of n nested principal minors (with dimensions 1 1, 2 2, : : : , n ... |