The problem of consistency for systems of linear equations and inequalities (Q911704)

A method for verifying the consistency of the problem \(Ax=b,\quad x\geq 0\) where \(A\in {\mathbb{R}}^{m\times n}\), \(b\in {\mathbb{R}}^ m\), \(b\neq 0\), and \(x\in {\mathbb{R}}^ n\) is given. The method requires a finite number of iterations and leads to a feasible point for consistent problems, otherwise a vector satisfying the inconsistency condition is obtained. The method works even in the degenerate case. The author mentions that his numerical experiments have shown finite termination.