An Efficient Algorithmic Procedure for Obtaining a Minimum $L_\infty $-Norm Solution to a System of Consistent Linear Equations

Abstract

Herein is described an algorithmic procedure for determining a minimum $l_\infty $-norm solution to the system of consistent linear equations \[ Ax = y,\] where A is a $m \times n$ matrix of rank m, y is a known $m \times 1$ vector and x is an unknown $n \times 1$ vector. The algorithm’s development is based on some fundamental concepts from functional analysis. Its computational efficiency is shown to easily exceed that of the linear programming formulization of the same problem.