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SYM-ILDL: Incomplete LDL^T Factorization of Symmetric Indefinite and Skew-Symmetric Matrices

Authors:

Paul LiuAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 44, Issue 1

Article No.: 1, Pages 1 - 21

https://doi.org/10.1145/3054948

Published: 11 April 2017 Publication History

Abstract

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 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, and MINRES, preconditioned with a symmetric positive definite preconditioner based on the ILDL factorization.

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Cited By

Rosen D(2022)Accelerating Certifiable Estimation with Preconditioned EigensolversIEEE Robotics and Automation Letters10.1109/LRA.2022.32201547:4(12507-12514)Online publication date: Oct-2022
https://doi.org/10.1109/LRA.2022.3220154
Ghannad AOrban DSaunders M(2021)Linear systems arising in interior methods for convex optimization: a symmetric formulation with bounded condition numberOptimization Methods and Software10.1080/10556788.2021.196559937:4(1344-1369)Online publication date: 8-Oct-2021
https://doi.org/10.1080/10556788.2021.1965599
Bharali RLarsson FJänicke R(2021)Computational aspects of the weak micro‐periodicity saddle point problemPAMM10.1002/pamm.20200025920:1Online publication date: 25-Jan-2021
https://doi.org/10.1002/pamm.202000259
Show More Cited By

Index Terms

SYM-ILDL: Incomplete LDL^T Factorization of Symmetric Indefinite and Skew-Symmetric Matrices
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices
  2. Mathematical software
    1. Mathematical software performance
    2. Solvers

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 44, Issue 1

March 2018

308 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/3071076

Editor:
Daniel Kressner
EPF Lausanne, Switzerland

Issue’s Table of Contents

Copyright © 2017 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 11 April 2017

Accepted: 01 December 2016

Revised: 01 November 2016

Received: 01 May 2015

Published in TOMS Volume 44, Issue 1

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Cited By

Rosen D(2022)Accelerating Certifiable Estimation with Preconditioned EigensolversIEEE Robotics and Automation Letters10.1109/LRA.2022.32201547:4(12507-12514)Online publication date: Oct-2022
https://doi.org/10.1109/LRA.2022.3220154
Ghannad AOrban DSaunders M(2021)Linear systems arising in interior methods for convex optimization: a symmetric formulation with bounded condition numberOptimization Methods and Software10.1080/10556788.2021.196559937:4(1344-1369)Online publication date: 8-Oct-2021
https://doi.org/10.1080/10556788.2021.1965599
Bharali RLarsson FJänicke R(2021)Computational aspects of the weak micro‐periodicity saddle point problemPAMM10.1002/pamm.20200025920:1Online publication date: 25-Jan-2021
https://doi.org/10.1002/pamm.202000259
Chen QGhai AJiao X(2021)HILUCSI: Simple, robust, and fast multilevel ILU for large‐scale saddle‐point problems from PDEsNumerical Linear Algebra with Applications10.1002/nla.240028:6Online publication date: 14-Jun-2021
https://doi.org/10.1002/nla.2400
Sanan PMay DBollhöfer MSchenk O(2020)Pragmatic solvers for 3D Stokes and elasticity problems with heterogeneous coefficients: evaluating modern incomplete LDL<sup><i>T</i></sup> preconditionersSolid Earth10.5194/se-11-2031-202011:6(2031-2045)Online publication date: 10-Nov-2020
https://doi.org/10.5194/se-11-2031-2020
Pearson JPestana J(2020)Preconditioners for Krylov subspace methods: An overviewGAMM-Mitteilungen10.1002/gamm.20200001543:4Online publication date: 21-Oct-2020
https://doi.org/10.1002/gamm.202000015
Manguoğlu MMehrmann V(2019)A Robust Iterative Scheme for Symmetric Indefinite SystemsSIAM Journal on Scientific Computing10.1137/18M119086041:3(A1733-A1752)Online publication date: 21-May-2019
https://doi.org/10.1137/18M1190860
Thuerck D(2019)Stretching Jacobi: Two-Stage Pivoting in Block-Based Factorization2019 IEEE/ACM 9th Workshop on Irregular Applications: Architectures and Algorithms (IA3)10.1109/IA349570.2019.00014(51-58)Online publication date: Nov-2019
https://doi.org/10.1109/IA349570.2019.00014

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