On the positivity of matrix-vector products Original Research Article

In this paper we examine the positivity of Rv where image, image, vgreater-or-equal, slanted0 with R=r(τA), r is a given (rational) function, image and τset membership, variant(0,∞). Here we mean by positivity the ordering w.r.t. an arbitrary order cone, which includes the classical entrywise positivity of vectors. Since the requirement Rgreater-or-equal, slanted0 leads to very severe restrictions on r and τ we construct a positive cone image and determine image such that image for all τset membership, variant[0,τ*]. Finally we give an example arising from applications to partial differential equations where our results explain actual computations much better than the general theory on Rgreater-or-equal, slanted0.