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.

References in zbMATH (referenced in 10 articles , 1 standard article )

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  1. Manguoğlu, Murat; Mehrmann, Volker: A two-level iterative scheme for general sparse linear systems based on approximate skew-symmetrizers (2021)
  2. Manguoğlu, Murat; Mehrmann, Volker: A robust iterative scheme for symmetric indefinite systems (2019)
  3. Wu, Lingfei; Xue, Fei; Stathopoulos, Andreas: TRPL+K: thick-restart preconditioned Lanczos+K method for large symmetric eigenvalue problems (2019)
  4. Scott, Jennifer; Tůma, Miroslav: A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows (2018)
  5. Gould, Nicholas; Scott, Jennifer: The state-of-the-art of preconditioners for sparse linear least-squares problems (2017)
  6. Greif, Chen; He, Shiwen; Liu, Paul: SYM-ILDL: Incomplete LDL(^\mathrmT) factorization of symmetric indefinite and skew-symmetric matrices (2017)
  7. Gupta, Anshul: Enhancing performance and robustness of ILU preconditioners by blocking and selective transposition (2017)
  8. Scott, Jennifer: On using Cholesky-based factorizations and regularization for solving rank-deficient sparse linear least-squares problems (2017)
  9. Scott, Jennifer; Tůma, Miroslav: Improving the stability and robustness of incomplete symmetric indefinite factorization preconditioners. (2017)
  10. Orban, Dominique: Limited-memory LDL(^\top) factorization of symmetric quasi-definite matrices with application to constrained optimization (2015)