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This paper proposes a new distributed algorithm for solving linear systemsassociated with a sparse graph under a generalised diagonal dominanceassumption. The algorithm runs iteratively on each node of the graph, with lowcomplexities on local information exchange between neighbouring nodes, localcomputation and local storage. For an acyclic graph under the condition ofdiagonal dominance, the algorithm is shown to converge to the correct solutionin a finite number of iterations, equalling the diameter of the graph. For aloopy graph, the algorithm is shown to converge to the correct solutionasymptotically. Simulations verify that the proposed algorithm significantlyoutperforms the classical Jacobi method and a recent distributed linear systemsolver based on average consensus and orthogonal projection.

A Fast Converging Distributed Solver for Linear Systems with Generalised Diagonal Dominance