Cholesky factorization algorithm

PLDL factorization of an n x n symmetric matrix A (where P is a permutation matrix) can be computed, say, by Aasen s algorithm, using about /6 (rather than n /3) flops and 0 n ) comparisons for pivoting, even if A is not positive definite and has no Choleski s factorization. 

Usually, the Jacobian matrix of the system (7.38) is nonsymmetric. Thus, it is neither possible to solve the linear system by means of the Cholesky algorithm nor to halve memory allocation. The most efficient methods (Gauss or PLR variant) adopted for Jacobian factorization require twice as much time and memory allocation as the Cholesky algorithm. 

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