An algorithm for non—negative least error minimal norm solutions

Abstract

In this paper we consider non-negative solutions of a system of m real 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 R n . 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 I P -norms (1 <p< ∞). Numerical results are also included.