Discrete-time distributed algorithms for solving linear equations via layered coordination

This paper is concerned with the problem of designing discrete-time distributed algorithms for solving large-scale linear equations via layered coordination. A row-column decomposition and a column-row decomposition are provided to partition the augmented matrix associated with the linear equations...

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Bibliographic Details
Published in:International journal of systems science Vol. 56; no. 3; pp. 638 - 657
Main Authors: Wang, Bo, Li, Jinghao
Format: Journal Article
Language:English
Published: London Taylor & Francis 17.02.2025
Taylor & Francis Ltd
Subjects:
Algorithms
Consensus
Coordination
Data exchange
Data integration
Decomposition
discrete-time distributed algorithm
layered coordination
Linear equations
Power flow
System effectiveness
ISSN:0020-7721, 1464-5319
Online Access:Get full text
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Summary:This paper is concerned with the problem of designing discrete-time distributed algorithms for solving large-scale linear equations via layered coordination. A row-column decomposition and a column-row decomposition are provided to partition the augmented matrix associated with the linear equations into several block matrices, respectively. By assigning an equation solver layer to computation and a data integration layer to data exchanges, a row-column decomposition-based discrete-time distributed algorithm and a column-row decomposition-based discrete-time distributed algorithm are proposed for solving large-scale linear equations, respectively. It is shown that the distributed algorithms proposed can reach a consensus exponentially on one of the solutions of linear equations. Finally, the effectiveness of the distributed algorithms proposed is validated via the numerical simulation of the power flow calculation of power systems and the problem of solving the large-scale linear equations.
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ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2024.2408539