Zusammenfassung
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.
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