  Contrary to an assumption made by Bojanczyk, Higham, and Patel [SIAM J.
Matrix Anal. Appl., 24(4):914-931, 2003], a perturbation bound for indefinite
least square problems is capable of arbitrarily large overestimates for all
perturbations of some problems. For these problems, the hyperbolic QR
factorization algorithm is not proved to be forward stable because the error
bound systematically overestimates the solution error of backward stable
methods.
