New perturbation bounds and condition numbers for the hyperbolic QR factorization
Hanyu Li, Peng Mei Lv · Linear and Multilinear Algebra · 2016
Using the modified matrix-vector equation approach, the technique of Lyapunov majorant function and the Banach fixed point theorem, we obtain some new rigorous perturbation bounds for R factor of the hyperbolic QR factorization under normwise perturbation. These bounds are always tighter than the one given in the literature. Moreover, the optimal first-order perturbation bounds and the normwise condition numbers for the hyperbolic QR factorization are also presented.