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

Bo Wang and Jinghao Li

International Journal of Systems Science, 2025, vol. 56, issue 3, 638-657

Abstract: 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.

Date: 2025
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DOI: 10.1080/00207721.2024.2408539

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