Gossip Algorithms that Preserve Privacy for Distributed Computation Part I: The Algorithms and Convergence Conditions

AbstractWe give a factorization formula to least-squares projection schemes, from which new convergence conditions together with formulas estimating the rate of convergence can be derived. We prove that the convergence of the method (including the rate of convergence) can be completely determined by the principal angles between {T^{\dagger}T(X_{n})} and {T^{*}T(X_{n})}, and the principal angles between {X_{n}\cap(\mathcal{N}(T)\cap X_{n})^{\perp}} and {(\mathcal{N}(T)+X_{n})\cap\mathcal{N}(T)^{\perp}}. At the end, we consider several specific cases and examples to further illustrate our theorems.

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Centered error entropy Kalman filter with application to satellite attitude determination

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211019867 ◽

2021 ◽

pp. 014233122110198

Author(s):

Baojian Yang ◽

Lu Cao ◽

Dechao Ran ◽

Bing Xiao

Keyword(s):

Kalman Filter ◽

Gaussian Noise ◽

Attitude Determination ◽

Complexity Analysis ◽

Iteration Algorithm ◽

Robust Algorithms ◽

Convergence Conditions ◽

Satellite Attitude ◽

Heavy Tailed ◽

Non Gaussian

Due to unavoidable factors, heavy-tailed noise appears in satellite attitude estimation. Traditional Kalman filter is prone to performance degradation and even filtering divergence when facing non-Gaussian noise. The existing robust algorithms have limited accuracy. To improve the attitude determination accuracy under non-Gaussian noise, we use the centered error entropy (CEE) criterion to derive a new filter named centered error entropy Kalman filter (CEEKF). CEEKF is formed by maximizing the CEE cost function. In the CEEKF algorithm, the prior state values are transmitted the same as the classical Kalman filter, and the posterior states are calculated by the fixed-point iteration method. The CEE EKF (CEE-EKF) algorithm is also derived to improve filtering accuracy in the case of the nonlinear system. We also give the convergence conditions of the iteration algorithm and the computational complexity analysis of CEEKF. The results of the two simulation examples validate the robustness of the algorithm we presented.

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Deadlock models in distributed computation

Proceedings of the 31st Annual ACM Symposium on Applied Computing - SAC '16 ◽

10.1145/2851613.2851880 ◽

2016 ◽

Cited By ~ 2

Author(s):

Valmir Carneiro Barbosa ◽

Alan Diêgo A. Carneiro ◽

Fábio Protti ◽

Uéverton S. Souza

Keyword(s):

Distributed Computation

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An iterative algorithm for the system of split mixed equilibrium problem

Demonstratio Mathematica ◽

10.1515/dema-2020-0027 ◽

2020 ◽

Vol 53 (1) ◽

pp. 309-324

Author(s):

Ibrahim Karahan ◽

Lateef Olakunle Jolaoso

Keyword(s):

Variational Inequality ◽

Iterative Algorithm ◽

Equilibrium Problems ◽

Nonexpansive Mappings ◽

Equilibrium System ◽

Convergence Conditions ◽

Mixed Equilibrium Problems ◽

Split Variational Inequality ◽

Mixed Equilibrium ◽

Split Mixed Equilibrium Problem

AbstractIn this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

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