Finite-Time Distributed Linear Equation Solver for Solutions With Minimum $l_1$-Norm

Zhou, Jingqiu; Wang, Xuan; Mou, Shaoshuai; Anderson, Brian D. O.

doi:10.1109/tac.2019.2932031

Cited by 18 publications

(2 citation statements)

References 48 publications

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“…2 also shows that Y e (t) finally converges a non-zero value, which implies that lim t→∞ ŷ(t) = 0. Based on the results of Theorem 1, we can verify that the obtained solution x * is not an exact solution of (14).…”

Section: B Simulationmentioning

confidence: 91%

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Distributed algorithms for the least square solution of linear equations

Huang,

Meng

2021

Preprint

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This paper proposes distributed algorithms for solving linear equations to seek a least square solution via multiagent networks. We consider that each agent has only access to a small and imcomplete block of linear equations rather than the complete row or column in the existing literatures. Firstly, we focus on the case of a homogeneous partition of linear equations. A distributed algorithm is proposed via a single-layered grid network, in which each agent only needs to control three scalar states. Secondly, we consider the case of heterogeneous partitions of linear equations. Two distributed algorithms with doubledlayered network are developed, which allows each agent's states to have different dimensions and can be applied to heterogeneous agents with different storage and computation capability. Rigorous proofs show that the proposed distributed algorithms collaboratively obtain a least square solution with exponential convergence, and also own a solvability verification property, i.e., a criterion to verify whether the obtained solution is an exact solution. Finally, some simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.

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Section: B Simulationmentioning

confidence: 91%

“…In this section, we show the effectiveness of the proposed algorithms ( 19) and ( 27) by solving the linear equation Ax = b in (14). Firstly, we consider the heterogeneous partition of Case 1 with…”

Section: Simulationmentioning

confidence: 99%