SYM-ILDL swMATH ID: 13375 Software Authors: Chen Greif, Shiwen He, Paul Liu Description: SYM-ILDL: Incomplete LDLT Factorization of Symmetric Indefinite and Skew-Symmetric Matrices. SYM-ILDL is a numerical software package that computes incomplete LDLT (or ‘ILDL’) factorizations of symmetric indefinite and 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 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, among other features. We also include an efficient MINRES implementation, applied with a specialized symmetric positive definite preconditioning technique based on the ILDL factorization. Homepage: http://www.cs.ubc.ca/~inutard/html/ Related Software: SparseMatrix; HSL; HSL_MI28; MA57; HSL_MA97; WSMP; LSMR; CUTEst; LSQR; Matlab; MINRES; PDCO; PARDISO; HSL_MA77; HSL_MA87; METIS; MUMPS; CHOLMOD; SuiteSparseQR; MIQR Cited in: 11 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year SYM-ILDL: Incomplete LDL\(^{\mathrm T}\) factorization of symmetric indefinite and skew-symmetric matrices. Zbl 1380.65061Greif, Chen; He, Shiwen; Liu, Paul 2017 all top 5 Cited by 13 Authors 4 Scott, Jennifer A. 2 Manguoglu, Murat 2 Mehrmann, Volker 2 Orban, Dominique 2 Tůma, Miroslav 1 Ghannad, Alexandre 1 Gould, Nicholas Ian Mark 1 Greif, Chen 1 Gupta, Anshul 1 He, Shiwen 1 Saunders, Michael A. 1 Stathopoulos, Andreas 1 Wu, Lingfei all top 5 Cited in 6 Serials 4 SIAM Journal on Scientific Computing 2 ACM Transactions on Mathematical Software 2 Numerical Algorithms 1 Numerical Linear Algebra with Applications 1 ETNA. Electronic Transactions on Numerical Analysis 1 Optimization Methods & Software Cited in 3 Fields 11 Numerical analysis (65-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Operations research, mathematical programming (90-XX) Citations by Year