Linear systems having nonnegative least squares solution

Abstract

Necessary conditions are developed for a system of the form Aλ=B with A≥0 and B≥ to have a least squares solution X which is nonnegative. Also it is shown that if a nonnegative matrix A has a nonnegative W-weighted { 1,3 -inverse for some nonnegative positive definite symmetric matrix W. then A has a nonnegative (1, 3) -inverse. As, a consequence of this, a short proof is obtained of a recent theorem of Jain and Egawa concerning nonnegative best approximate solutions (SIAM J. ALG. DISC. METH., 3 (1982), 197-213).