Perturbation analysis for the generalized Cholesky factorization

Let K be a symmetric indefinite matrix. Suppose that K=LJL^T is the generalized Cholesky factorization of K. In this paper we present perturbation analysis for the generalized Cholesky factorization. We obtain the first-order bound on the norm of the perturbation in the generalized Cholesky factor. Also, we give rigorous perturbation bounds.