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Summary A symmetric scaling of a nonnegative, square matrixA is a matrixXAX-1, whereX is a nonsingular, nonnegative diagonal matrix. By associating a family of weighted directed graphs with the matrixA we are able to adapt the shortest path algorithms to compute an optimal scaling ofA, where we call a symmetric scalingA' ofA optimal if it minimizes the maximum of the ratio of non-zero elements.

Applications of shortest path algorithms to matrix scalings