On optimal backward perturbation bounds for the linear least squares problem (Q678224)

The paper considers the linear least squares problem \(\min_x |b-Ax |_2\), where \(A\) is an \(m\times n\) matrix \((m>n)\) and \(b\) is an \(m\)-dimensional vector. It is shown that \(\inf|F|_2\) on the set of the solutions and that on the minimum 2-norm solutions to \(\min_x |b- (A+F)x |_2\) are identical.