Two-sided generalized hyperbolic QR factorization and its perturbation analysis

Abstract

We first propose the two-sided generalized hyperbolic QR factorization of a matrix pair, which is a generalization of the generalized QR factorization. More explicitly, two orthogonal matrices in the generalized QR factorization are replaced with two corresponding J-orthogonal matrices, where J is a signature matrix. Then, we consider the perturbation analysis of the new matrix factorization. Some first order normwise perturbation bounds are derived using the refined matrix equation approach and the updated matrix–vector equation approach. The corresponding perturbation bounds for the generalized QR factorization are also obtained as the special case. In comparison, these bounds can be much tighter than the previous ones derived from Barrlund (1994) [A. Barrlund, Perturbation bounds for the generalized QR factorization, Linear Algebra Appl. 207 (1994) 251–271].