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A solution of a tropical linear vector equation (1212.6107v1)
Published 26 Dec 2012 in math.OC and cs.DM
Abstract: A linear vector equation is considered defined in terms of idempotent mathematics. To solve the equation, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces and reduces the solution of the equation to that of a tropical optimization problem. Based on the approach, existence and uniqueness conditions are established for the solution, and a general solution to the equation is given.