A row space method for solving a system of linear equations

Abstract

A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In addition, the algorithm permits an online formulation so that computations may proceed as the data become available. The algorithm does not require the solution of a triangular system of equations, nor does it rely on block partitioned matrices.