Factorizing symmetric indefinite matrices

AbstractThe LDLT factorization of a symmetric indefinite matrix, although efficient computationally, may not exist and can be unstable in the presence of round off error. The use of block diagonal 2×2 pivots is attractive, but there are some difficulties in determining an efficient and stable pivot strategy. Previous suggestions have required O(n>3) operations (either multiplications or comparisons) just to implement the pivot strategy. A new strategy is described which in practice only requires O(n2) operations. Indeed, the effort required by this pivot strategy is less than that required when using partial pivoting with an unsymmetric LU factorization, which is the usual way of factorizing indefinite matrices