An algorithm for non—negative least error minimal norm solutions

Abstract

In this paper we consider non—negative solutions of a system of m reai linear equations, Ax = b, in n unknowns which minimize the residual error when R^m is equipped with a strictly convex norm. Out of these solutions we seek the one which is of the least norm for a strictly convex and smooth norm on Rⁿ. An implementable iterative algorithm accomplishing this is given. The algorithm is globally convergent and it does not require that a non—negative least error solution be found first. As a special case, we test the algorithm for the l^p—norms (1<p<∞). Numerical results are also included