A theory for parametric linear systems

Abstract

We present a theoretical foundation for studying parametric systems of hrtear 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 s eciahzed systems may be given uniformly. For homogeneous sYstems, or for systetns where the right hand side is arbitrary, thn small set is irredundant. We also give a complexity analysis of the Gaussian elimination rnethocl and compare that with our algorithm.