On Sparse Reflexive Generalized Inverses

Abstract We study sparse generalized inverses H of a rank- r real matrix A . We give a construction for reflexive generalized inverses having at most r 2 nonzeros. For r = 1 and for r = 2 with A nonnegative, we demonstrate how to minimize the (vector) 1-norm over reflexive generalized inverses. For general r , we efficiently find reflexive generalized inverses with 1-norm within approximately a factor of r 2 of the minimum 1-norm generalized inverse.