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The generalized nested dissection method, developed by Lipton, Rose, and Tarjan, is a seminal method for solving a linear system $Ax=b$ where $A$ is a symmetric positive definite matrix. The method runs extremely fast whenever $A$ is a well-separable matrix (such as matrices whose underlying support is planar or avoids a fixed minor). In this work we extend the nested dissection method to apply to {em any} non-singular well-separable matrix over {em any} field. The running times we obtain essentially match those of the nested dissection method.

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