A note on the perturbation analysis for the generalized Cholesky factorization

In this note, we consider the perturbation analysis for the generalized Cholesky factorization further. The conditions for the main theorems of the paper [W.-G. Wang, J.-X. Zhao, Perturbation analysis for the generalized Cholesky factorization, Appl. Math. Comput. 147 (2004) 601–606] are weakened by using an alternative method. Moreover, some new perturbation bounds are also derived.