AN INVERSE STRUCTURED PERTURBATION PROBLEM FOR THE LINEAR SYSTEM AT Ax = b
Marek Szularz, Alicja Smoktunowicz, Ewa Pawelec · Demonstratio Mathematica · 2010
The paper deals with the following inverse perturbation problem for the linear system A T Ax = b: assuming that there exist two (possibly different) perturbations Ei and E2 of A so that (A + E2) T (A + E\)y = b, we ask whether there is a single perturbation F of A so that (A + F) r {A + F)y = b.We consider only small relative normwise perturbations of A. It is shown that if y T b > 0 and a>(y) -^j^Jj^2 is small, then our problem has a solution.Some practical upper and lower error bounds for the structured backward error are also given.