Convergence of the D-iteration algorithm: convergence rate and asynchronous distributed scheme

Dohy Hong 1, 2 Fabien Mathieu 2, 3 Gérard Burnside 1
3 GANG - Networks, Graphs and Algorithms
LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications, Inria Paris-Rocquencourt
Abstract : In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We show how this can be applied to prove and improve the convergence of a fixed point problem associated to the matrix iteration scheme, including for distributed computation framework. The approach can be understood as a decomposition of the matrix-vector product operation in elementary operations at the vector entry level.
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https://hal.inria.fr/hal-00776084
Contributor : Dohy Hong <>
Submitted on : Friday, January 18, 2013 - 2:55:49 PM
Last modification on : Tuesday, May 14, 2019 - 10:15:50 AM

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  • HAL Id : hal-00776084, version 1
  • ARXIV : 1301.3007

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Dohy Hong, Fabien Mathieu, Gérard Burnside. Convergence of the D-iteration algorithm: convergence rate and asynchronous distributed scheme. [Research Report] 2013, pp.9. ⟨hal-00776084⟩

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