Bounds for perturbed solutions of linear operator equations in Hilbert space.
Let \(X\), \(Y\) be two Hilbert spaces and \(A: X\to Y\) be a bounded linear operator with closed range. The authors consider the system of one operator equation \(Ax= b\) and the perturbed equation \((A+ E)y= b+e\). Under the assumption that the system is consistent, they present lower and upper bounds on relative errors for perturbed solutions. Perturbation results on relative errors are also given for weighted least squares problems with the help of weighted generalized inverses.
scientific article; zbMATH DE number 1861212