Abstract
In this paper, we discuss and analyze methods for solving a system of linear equations over idempotent semifields. The first method is based on the pseudo-inverse of the system matrix. We then go over a specific version of Cramer’s rule which is also related to the pseudo-inverse of the system matrix. In these two methods, the constant vector plays an implicit role in solvability of the system. Another method is called the normalization method in which both the system matrix and the constant vector play explicit roles in the solution process. Each of these methods yields the maximal solution if it exists. Importantly, we show that the maximal solutions obtained from these methods as well as the previously studied LU-method are all identical.
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