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A linear system of equations for which its matrix of coefficients A can be decomposed into k separate blocks of coefficients Ai, where each Ai represents the coefficients of a different set of equations. This structure typically represents a system consisting of k subsystems whose activities are almost autonomous, except for a few top-level system constraints whose variables couple the k blocks of the subsystems. Such systems can also have a few variables external to the blocks that couple the blocks. Dantzig-Wolfe decomposition algorithm; Large-scale systems; Weakly-coupled systems.