^{T}Factorization of Symmetric Indefinite and Skew-Symmetric Matrices

SYM-ILDL is a numerical software package that computes incomplete LDL^{T} (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 [2005]. Our code is economical in terms of storage, and it deals with real skew-symmetric matrices as well as symmetric ones. The package is written in C++ and is templated, is open source, and includes a M^{™}

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^{T}factorization of symmetric quasi-definite matrices with application to constrained optimization. Numerical Algorithms 70, 1, 9--41.