Literature about used hessian aproximation


Could you help me with literature links?
Dynare computes standard deviations for estimated parameters. Dynare compute finite difference approximation of log-likelihood functions Hessian. After that “the Gill-Murray generalized choleski decomposition” is used for transformation of computed Hessian. It makes matrix to be positive define, as I understand. Where could I find reasons for such transformation? Could it lead to asymptotically biased estimator of covariance matrix?

Thank you for your response