  We propose a new inertia-revealing factorization for sparse symmetric
matrices. The factorization scheme and the method for extracting the inertia
from it were proposed in the 1960s for dense, banded, or tridiagonal matrices,
but they have been abandoned in favor of faster methods. We show that this
scheme can be applied to any sparse symmetric matrix and that the fill in the
factorization is bounded by the fill in the sparse QR factorization of the same
matrix (but is usually much smaller). We describe our serial proof-of-concept
implementation, and present experimental results, studying the method's
numerical stability and performance.
