An algorithm is presented to compute a triangular factorization and the inertia of a symmetric matrix. The algorithm is stable even when the matrix is not positive definite and is as fast as Choleski. Programs for solving associated system of linear equations are included.
Bunch, James R.; Kaufman, Linda; and Parlett, Beresford N., "Decomposition of a Symmetric Matrix ; CU-CS-080-75" (1975). Computer Science Technical Reports. 78.