2015/05/28 by Chen Greif, Greif, Chen, Shiwen He +3
Computer Science · Physics and Astronomy · #Electromagnetic Scattering and Analysis #F.2.1 #FOS: Computer and information sciences #FOS: Mathematics #G.1.0 #G.1.3 #Mathematical Software (cs.MS) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Parallel Computing and Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1505.07589
openalex publication_date 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
SYM-ILDL is a numerical software package that computes incomplete LDLT (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.