Perturbation theory for the generalized inverse \(A_{T,S}^{(2)}\) (Q2706700)

A perturbation theory for the generalized inverse \(A_{T,s}^{(2)} \) is developed using a decomposition of \(B_{T,S}^{(2)}- A_{T,S}^{(2)}\) under the assumption that the \((W)\)-condition holds. The norm of \(\|B_{T,S}^{(2)}-A_{T,S}^{(2)}\|\) is estimated for every multiplicative norm when \((W)\)-condition holds and \(\|B-A\|\) is small. A perturbation bound for the unique solution of the general restricted system \(Ax=b\), \(b\in AT\), \(\dim(AT)= \dim(T)\), is given. As an illustrative example the numerical value of \(A^{(2)}_{T,S}\) is calculated for a matrix \(A\).