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An inverse structured perturbation problem for the linear system ATAx = b

Szularz M., Smoktunowicz A., Pawelec E.

Demonstratio Mathematica

2010

Vol. 43, nr 4

755-763

The paper deals with the following inverse perturbation problem for the linear system ATAx = b: assuming that there exist two (possibly different) perturbations E1 and E2 of A so that (A + E2)T (A + E1)y = b, we ask whether there is a single perturbation F of A so that (A + F)T (A + F)y = b. We consider only small relative normwise perturbations of A. It is shown that if yT b >0 and (...) is small, then our problem has a solution. Some practical upper and lower error bounds for the structured backward error are also given.