The explicit formula for Gauss-Jordan elimination applied to flexible systems (Q2148851)

This study focuses on the solution of the so-called flexible systems of linear equations, where the traditional linear algebraic system \(Ax=b\) is extended by adding error terms to each of the entry of the data \(A,b\) to model their imprecision. The solution is then represented by a set of vectors \(x\). First, stability conditions are formulated ensuring that data errors are of reasonable size. Then, a Gauss-Jordan elimination procedure is described providing a mathematical framework to obtain a set of solutions \(x\) for the flexible system. Small illustrative examples are included to illustrate the results. The paper is nicely structured.