Just read about https://arxiv.org/abs/2203.03456 in Quanta artical https://www.quantamagazine.org/finally-a-fast-algorithm-for-shortest-paths-on-negative-graphs-20230118/. One of the algorithms used in the solution computes a low-diameter decomposition of the graph, identifying groups of nodes which are "close" to each other. The phrase "strongly connected components" appeared in the discussion and that got me wondering if such graph analysis might be applied to systems of equations to identify groups of equations that could be partially solved in isolation of others (for a sparse matrix).
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