Under certain conditions, K is quasi-definite. 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. 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.
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