Quasi-definite matrices have been used successfully by Vanderbei within barrier methods for linear and quadratic programming. An advantage is that for a sequence of K's, P may be chosen once and for all to optimize the sparsity of L, as in the positive-definite case.
A preliminary stability analysis is developed here. It is observed that a quasi-definite matrix is closely related to an unsymmetric positive-definite matrix, for which an LDM' factorization exists. Using Golub and Van Loan's analysis of the latter, conditions are derived under which Cholesky factorization is stable for quasi-definite systems. Some numerical results confirm the predictions.