An algorithm for solving parametric linear systems

Abstract

We present a theoretical foundation for studying parametric systems of linear equations and prove an efficient algorithm for identifying all parametric values (including degenerate cases) for which the system is consistent. The algorithm gives a small set of regimes where for each regime, the solutions of the specialized systems may be given uniformly. For homogeneous linear systems, or for systems where the right hand side Is arbitrary, this small set is irredundant. We discuss in detail practical issues concerning implementations, with particular emphasis on simplification of results, Examples are given based on a close implementation of the algorithm in SCRATCHPAD II. We also give a complexity analysis of the Gaussian elimination method and compare that with our algorithm.