Unattainability of A Perturbation Bound for Indefinite Linear Least Squares Problems

Abstract

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.

9 pages

Cited by in corpus (2)

• Backward error and condition number analysis for the indefinite linear least squares problem
• On the partial condition numbers for the indefinite least squares problem