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A scheme for robust distributed sensor fusion based on average consensus
 Proceedings of the International Conference on Information Processing in Sensor Networks (IPSN
, 2005
"... Abstract — We consider a network of distributed sensors, where each sensor takes a linear measurement of some unknown parameters, corrupted by independent Gaussian noises. We propose a simple distributed iterative scheme, based on distributed average consensus in the network, to compute the maximum ..."
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Cited by 146 (3 self)
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Abstract — We consider a network of distributed sensors, where each sensor takes a linear measurement of some unknown parameters, corrupted by independent Gaussian noises. We propose a simple distributed iterative scheme, based on distributed average consensus in the network, to compute the maximumlikelihood estimate of the parameters. This scheme doesn’t involve explicit pointtopoint message passing or routing; instead, it diffuses information across the network by updating each node’s data with a weighted average of its neighbors ’ data (they maintain the same data structure). At each step, every node can compute a local weighted leastsquares estimate, which converges to the global maximumlikelihood solution. This scheme is robust to unreliable communication links. We show that it works in a network with dynamically changing topology, provided that the infinitely occurring communication graphs are jointly connected. I.
Row Projection Methods For Large Nonsymmetric Linear Systems
 SIAM J. Scientific and Statistical Computing
, 1992
"... . Three conjugate gradient accelerated row projection (RP) methods for nonsymmetric linear systems are presented and their properties described. One method is based on Kaczmarz's method and has an iteration matrix that is the product of orthogonal projectors; another is based on Cimmino's ..."
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Cited by 42 (5 self)
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. Three conjugate gradient accelerated row projection (RP) methods for nonsymmetric linear systems are presented and their properties described. One method is based on Kaczmarz's method and has an iteration matrix that is the product of orthogonal projectors; another is based on Cimmino's method and has an iteration matrix that is the sum of orthogonal projectors. A new RP method which requires fewer matrixvector operations, explicitly reduces the problem size, is error reducing in the 2norm, and consistently produces better solutions than other RP algorithms is also introduced. Using comparisons with the method of conjugate gradient applied to the normal equations, the properties of RP methods are explained. A row partitioning approach is described which yields parallel implementations suitable for a wide range of computer architectures, requires only a few vectors of extra storage, and allows computing the necessary projections with small errors. Numerical testing verifies the robu...
Infinite Products And Paracontracting Matrices
 Electronic Journal of Linear Algebra
, 1997
"... Introduction. In the investigation of chaotic iteration procedures for linear consistent systems matrices which are paracontracting with respect to some vector norm play an important role. It was shown in [EKN], that if A 1 ; : : : ; Am are finitely many kbyk complex matrices which are paracont ..."
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Cited by 12 (3 self)
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Introduction. In the investigation of chaotic iteration procedures for linear consistent systems matrices which are paracontracting with respect to some vector norm play an important role. It was shown in [EKN], that if A 1 ; : : : ; Am are finitely many kbyk complex matrices which are paracontracting with respect to the same norm, then for any sequence d i ; 1 d i m; i = 1; 2; : : : and any x 0 the sequence x i+1 = A d i x i i = 1; 2; : : : is convergent. In particular A (d) = lim i!1 A d i : : : A d1 exists for all sequences fd i g
Convergence of infinite products of matrices and innerouter iteration schemes,” Electron
 Trans. Numer. Anal
, 1994
"... Dedicated to Wilhelm Niethammer on the occasion of his sixtieth birthday. Abstract. We develop conditions under which a product ∏∞ i=0 Ti of matrices chosen from a possibly infinite set of matrices S = {Tjj ∈ J} converges. We obtain the following conditions which are sufficient for the convergence ..."
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Cited by 10 (0 self)
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Dedicated to Wilhelm Niethammer on the occasion of his sixtieth birthday. Abstract. We develop conditions under which a product ∏∞ i=0 Ti of matrices chosen from a possibly infinite set of matrices S = {Tjj ∈ J} converges. We obtain the following conditions which are sufficient for the convergence of the product: There exists a vector norm such that all matrices in S are nonexpansive with respect to this norm and there exists a subsequence {ik} ∞ k=0 of the sequence of the nonnegative integers such that the corresponding sequence of operators { } ∞ Tik k=0 converges to an operator which is paracontracting with respect to this norm. We deduce the continuity of the limit of the product of matrices as a function of the sequences {ik} ∞ k=0. But more importantly, we apply our results to the question of the convergence of inner–outer iteration schemes for solving singular consistent linear systems of equations, where the outer splitting is regular and the inner splitting is weak regular.
Distributed Average Consensus with TimeVarying Metropolis Weights
, 2006
"... Given a network of processes where each node has an initial scalar value, we consider the problem of computing their average asymptotically using a distributed, linear iterative algorithm. At each iteration, each node replaces its own value with a weighted average of its previous value and the value ..."
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Cited by 7 (0 self)
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Given a network of processes where each node has an initial scalar value, we consider the problem of computing their average asymptotically using a distributed, linear iterative algorithm. At each iteration, each node replaces its own value with a weighted average of its previous value and the values of its neighbors. We introduce the Metropolis weights, a simple choice for the averaging weights used in each step. We show that with these weights, the values at every node converge to the average, provided the infinitely occurring communication graphs are jointly connected.
Interpretational Abstraction, in
 Computers and Mathematics with Applications, Pergamon Press
, 1991
"... A majority of cortical areas are connected via feedforward and feedback fiber projections. The computational role of the descending feedback pathways at different processing stages remains largely unknown. We suggest a new computational model in which normalized activities of orientation selective c ..."
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Cited by 1 (1 self)
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A majority of cortical areas are connected via feedforward and feedback fiber projections. The computational role of the descending feedback pathways at different processing stages remains largely unknown. We suggest a new computational model in which normalized activities of orientation selective contrast cells are fed forward to the next higher processing stage. The arrangement of input activation is matched against local patterns of curvature shape to generate activities which are subsequently fed back to the previous stage. Initial measurements that are consistent with the topdown generated contextdependent responses are locally enhanced. In all, we present a computational theory for recurrent processing in visual cortex in which the significance of measurements is evaluated on the basis of priors that are represented as contour code patterns. The model handles a variety of perceptual phenomena, such as e.g. bar texture stimuli, illusory contours, and grouping of fragmented shape outline. 1
Partial Norms and the Convergence of General Products of Matrices
, 1997
"... Motivated by the theory of inhomogeneous Markov chains, we determine a sufficient condition for the convergence to 0 of a general product formed from a sequence of real or complex matrices. When the matrices have a common invariant subspace H, we give a sufficient condition for the convergence to 0 ..."
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Motivated by the theory of inhomogeneous Markov chains, we determine a sufficient condition for the convergence to 0 of a general product formed from a sequence of real or complex matrices. When the matrices have a common invariant subspace H, we give a sufficient condition for the convergence to 0 on H of a general product. Our result is applied to obtain a condition for the weak ergodicity of an inhomogeneous Markov chain. We compare various types of contractions which may be defined for a single matrix, such as paracontraction, lcontraction, and Hcontraction, where H is an invariant subspace of the matrix.
ELA INFINITE PRODUCTS AND PARACONTRACTING MATRICES
"... Abstract. In [Linear Algebra Appl., 161:227{263, 1992] the LCPproperty of a nite set of square complex matrices was introduced and studied. A set is an LCPset if all left in nite products formed from matrices in are convergent. It was shown earlier in [Linear Algebra Appl., 130:65{82, 1990] that a ..."
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Abstract. In [Linear Algebra Appl., 161:227{263, 1992] the LCPproperty of a nite set of square complex matrices was introduced and studied. A set is an LCPset if all left in nite products formed from matrices in are convergent. It was shown earlier in [Linear Algebra Appl., 130:65{82, 1990] that a set paracontracting with respect to a xed norm is an LCPset. Here a converse statement isproved: If is an LCPset with a continuous limit function then there exists a norm such that all matrices in are paracontracting with respect to this norm. In addition the stronger property of `paracontractivity isintroduced. It is shown that common `paracontractivity of a set of matrices has a simple characterization. It turns out that in the above mentioned converse statement the norm can be chosen such that all matrices are `paracontracting. It is shown that for consisting of two projectors the LCPproperty is equivalent to `paracontractivity, even without requiring continuity. AMS(MOS) subject classi cation. 65F10, 47H09, 15A99 Key words. Convergence, in nite products, LCPproperty, product boundedness, paracontracting matrices, norms, projections 1. Introduction. In
DOI: 10.1109/TAC.2010.2054950 On the Convergence of Linear Switched Systems
, 2012
"... Abstract—This paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems. We provide a collection of results that use weak dwelltime, dwelltime, strong dwelltime, permanent and persistent activation hypothesis. The obtained results are shown ..."
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Abstract—This paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems. We provide a collection of results that use weak dwelltime, dwelltime, strong dwelltime, permanent and persistent activation hypothesis. The obtained results are shown to be tight by counterexample. Finally, we apply our result to the threecell converter. Index Terms—Switched systems, dwelltime, stability, omegalimit set, threecell converter.