New Perturbation Analysis for the Generalized Cholesky Factorization

Suppose real symmetric matrix has the generalized Cholesky factorization,it is proved that the generalized Cholesky factorization of perturbing matrix satisfies:‖△L‖F/‖L‖2≤Kc(K)e+O(e3).One example shows that this perturbation result is more precise than ever.