  SYM-ILDL is a numerical software package that computes incomplete $LDL^{T}$
(or `ILDL') factorizations of symmetric indefinite and real skew-symmetric
matrices. The core of the algorithm is a Crout variant of incomplete LU (ILU),
originally introduced and implemented for symmetric matrices by [Li and Saad,
Crout versions of ILU factorization with pivoting for sparse symmetric
matrices, Transactions on Numerical Analysis 20, pp. 75--85, 2005]. Our code is
economical in terms of storage and it deals with real skew-symmetric matrices
as well, in addition to symmetric ones. The package is written in C++ and it is
templated, open source, and includes a MATLAB interface. The code includes
built-in RCM and AMD reordering, two equilibration strategies, threshold
Bunch-Kaufman pivoting and rook pivoting, as well as a wrapper to MC64, a
popular matching based equilibration and reordering algorithm. We also include
two built-in iterative solvers: SQMR preconditioned with ILDL, or MINRES
preconditioned with a symmetric positive definite preconditioner based on the
ILDL factorization.
