Sparsity-Preserving Difference of Positive Semidefinite Matrix   Representation of Indefinite Matrices
  We consider the problem of writing an arbitrary symmetric matrix as the difference of two positive semidefinite matrices. We start with simple ideas such as eigenvalue decomposition. Then, we develop a simple adaptation of the Cholesky that returns a difference-of-Cholesky representation of indefinite matrices. Heuristics that promote sparsity can be applied directly to this modification. 
Jaehyun Park
math.NA cs.NA