On the convergence of asynchronous paracontractions with application to tomographic reconstruction from incomplete data

Elsner, Ludwig; Koltracht, I.; Neumann, Michael

doi:10.1016/0024-3795(90)90206-r

Cited by 74 publications

(45 citation statements)

References 5 publications

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“…The property that is established in lemma 1 is referred to in the literature as the paracontracting property; see [24] chapter 8 or [25]. We have thus shown that the matrices M i are paracontractive in S in L 1 norm.…”

Section: Remarkmentioning

confidence: 60%

Tools for the analysis and design of communication networks with Markovian dynamics

Leizarowitz

Stanojevic

Shorten

2006

IEE Proceedings - Control Theory and Applications

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Abstract:The stochastic properties of a class of communication networks whose dynamics are Markovian are analysed. The asymptotic behaviour of such a network in terms of the first and second moments of a stochastic process that describes the network dynamics is characterised and tools for their calculation are provided. Specifically, computation techniques for the calculation of these statistics are provided and that these algorithms converge exponentially fast is shown. Finally, how the results may be used for the design of network routers to realise networks with desired statistical properties is suggested. Introduction General remarksThe study of communication networks that carry transmission control protocol (TCP) traffic has been subject of intense interest in the computer science, network engineering, and applied mathematics literature [1 -9]. The principal motivation for much of this work has been to understand network behaviour, and to characterise important network properties with a view to developing analytic tools for the design of such networks. In particular, much of this work has focussed on understanding the manner in which the network allocates available bandwidth among competing network flows (network fairness) and the speed at which this bandwidth allocation takes place (network convergence rate). Recently, a very accurate random matrix model of TCP network dynamics was proposed [10]. This model was shown to be capable of capturing many essential features of networks in which TCP-like network flows compete for bandwidth via a bottleneck router. By making some simplifying assumptions concerning stochastic behaviour of the network, the authors demonstrate that this model may also be used as a basis to design networks in which bandwidth can be allocated in an arbitrary manner among competing flows. This may be achieved by redesigning the manner in which individual sources respond to network congestion, or by redesigning the manner in which network routers respond to network congestion (or both).The objective of this paper is to pursue further this line of research. However, rather than using the model as a basis for adjusting the behaviour of the individual flows to achieve desired network behaviour, we concentrate here on using this model to redesign the manner in which the bottleneck router drops packets when the network is congested; in particular, we analyse the properties of such networks when the bottleneck router drops packets according to some Markovian rules. Redesigning the manner in which network routers operate to allocate bandwidth is very important for a number of reasons related to network quality of service issues. Whereas the results in [10] are interesting from a theoretical perspective, router redesign along the lines suggested by this work would place an impossible computational burden on the network routers; on the other hand, dropping packets according to some Markovian rule could possibly be implemented using far fewer computational resources. Our principal contribution in t...

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Section: Remarkmentioning

confidence: 60%

Tools for the analysis and design of communication networks with Markovian dynamics

Leizarowitz

Stanojevic

Shorten

2006

IEE Proceedings - Control Theory and Applications

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“…. , n. Therefore, we have P x ≤ P x = x , ∀x ∈ R n , which proves P is a paracontracting matrix [15]. For a paracontracting matrix M , we denote H(M ) as its fixed-point subspace, i.e., H(M ) = {x|x ∈ R n |Mx = x}.…”

Section: Discussionmentioning

confidence: 91%

“…On the other hand, because E s is invariant under all P i(k) [16], the sequence of vectors given by w(k +1) = P i(k) w(k) all belong to E s which leads to the limit w * ∈ E s . From the properties of the infinite paracontracting process [15], w * has to be in the fixed subspace of r i=1 H(P i ). It means w * ∈ span{1} = E 1 , which yields w * = 0, because E 1 E s = ∅.…”

Section: Discussionmentioning

confidence: 99%

Distributed Cooperative Spectrum Sensing Based on Weighted Average Consensus

Zhang

Wang

Guo

et al. 2011

2011 IEEE Global Telecommunications Conference - GLOBECOM 2011

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Abstract-In this paper, we study the distributed spectrum sensing in cognitive radio networks. Using weighted average consensus algorithm, we develop a weighted soft measurement combining scheme without the centralized fusion center. After the measurement by the energy detector, each secondary user (SU) exchanges their own measurement statistics with its local neighbors, and chooses the information exchanging rate according to the estimated average signal-to-noise ratio (SNR). We prove the convergence of the consensus iteration, and each SU will hold the global decision statistics from the weighted soft measurement combining throughout the network. The proposed scheme is robust with respect to temporary communication link failures. Simulation results show our method has a better performance than the existing average consensus-based approach.

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“…Niu et al [15] present Hogwild!, which is an asynchronous stochastic gradient descent algorithm. Elsener, Koltracht and Neumann present a shared memory asynchronous implementation of Kaczmarz method for solving linear equations [8], which more recently has been restudied in the distributed memory setting by Liu, Wright and Sridhar [13]. Lu and Tang [14] propose an algorithm for solving systems with symmetric positive definite matrices over a network of asynchronous agents, whose interactions are controlled by some (random) external network dynamics.…”

Section: X[i](k)=m[ii]*x[i](k-1)+c[i] For All Inputs J X[i](k)=x[i](kmentioning

confidence: 99%

Performance analysis of asynchronous parallel Jacobi

Hook

Dingle

2017

Numer Algor

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The directed acyclic graph (DAG) associated with a parallel algorithm captures the partial order in which separate local computations are completed and how their outputs are subsequently used in further computations. Unlike in a synchronous parallel algorithm the DAG associated with an asynchronous parallel algorithm is not predetermined. Instead it is a product of the asynchronous timing dynamics of the machine and cannot be known in advance, as such it is best thought of as a pseudorandom variable.In this paper we present a formalism for analyzing the performance of asynchronous parallel Jacobi's method in terms of its DAG. We use this approach to prove error bounds and bounds on the rate of convergence. The rate of convergence bounds are based on the statistical properties of the DAG and are valid for systems with a non-negative iteration matrix. We support our theoretical results with a suit of numerical examples, where we compare the performance of synchronous and asynchronous parallel Jacobi to certain statistical properties of the DAGs associated with the computations. We also present some examples of small matrices with elements of mixed sign, which demonstrate that determining whether a system will converge under asynchronous iteration in this more general setting is a far more difficult problem.

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On the convergence of asynchronous paracontractions with application to tomographic reconstruction from incomplete data

Cited by 74 publications

References 5 publications

Tools for the analysis and design of communication networks with Markovian dynamics

Tools for the analysis and design of communication networks with Markovian dynamics

Distributed Cooperative Spectrum Sensing Based on Weighted Average Consensus

Performance analysis of asynchronous parallel Jacobi

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