A new iterative method for solving non-square systems of linear equations

This technical note presents a new iterative procedure for solving systems of m linear equations in n variables under a sufficient condition that is practical. We show how this procedure may utilize elementary row operations to meet its sufficient condition. In this iterative procedure, the approximate solution obtained in each iteration is a convex combination of some l∞-norm projections of the previous approximate solution. Under a regularity condition, this procedure converges quadratically. Application examples are given that show how this procedure can generate desired non-basic solutions and how it can aid Fourier-Motzkin elimination method in solving linear programming problems.