Comprehensive LU Decomposition and True Path

We study the PLU decomposition of rectangular matrices with polynomial coefficients, depending on parameters, possibly subject to algebraic constraints. Computing such a parametric decomposition typically requires to split computations into cases. This yields various computational challenges, in particular the fact that more cases than necessary may be generated. In this paper, we present heuristic methods which attempt to minimize the number of cases. In particular, these methods try to avoid splitting the computations, if this is possible. We implemented these methods in Maple and evaluated their benefits on various test problems coming from the literature.