Factorizing symmetric indefinite matrices

The LDL^T 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.