This library implements a set of useful algebraic (incomplete factorization-based) preconditioners that can be used to accelerate the convergence of many iterative numerical linear-algebraic algorithms (such as the conjugate gradient, Lanczos, or LOBPCG methods). It builds upon the incomplete Crout symmetric indefinite LDL' factorization provided by the sym-ildl library, extending its functionality to implement inertia correction (so that the constructed preconditioners are positive-definite, as required by many inexact linear-algebraic methods), as well as presenting an interface that permits easy integration with Eigen.

This library can be built and exported as a CMake project. The following installation instructions have been verified on Ubuntu 22.04:

Step 1: Install dependencies

$ sudo apt-get install build-essential cmake-gui libeigen3-dev liblapack-dev libblas-dev libsuitesparse-dev

Step 2: Clone the repository

$ git clone https://github.com/david-m-rosen/Preconditioners Preconditioners

Step 3: Create build directory

$ cd Preconditioners && mkdir build

Step 4: Configure build and generate Makefiles

$ cd build && cmake ..

Step 5: Build the library

$ make -j

We are making this software freely available in the hope that it will be useful to others. If you use our code in your own work, please cite our paper, which describes the design of the inertia-corrected incomplete symmetric indefinite preconditioner implemented in the ILDL class:

@misc{Rosen2022Accelerating,
  title = {Accelerating Certifiable Estimation with Preconditioned Eigensolvers},
  author = {Rosen, David M.},
  month = may,
  year = {2022},
  publisher = {arXiv},
  doi = {10.48550/ARXIV.2207.05257},
  url = {https://arxiv.org/abs/2207.05257},
}

and the following paper of Greif et al., which describes the design of the sym-ildl library that this project includes:

@article{Greif2017SymILDL,
title = {{SYM-ILDL}: Incomplete {$LDL\transpose$} Factorization of Symmetric Indefinite and Skew-Symmetric Matrices},
author = {Greif, C. and He, S. and Liu, P.},
journal = {{ACM} Trans. Math. Softw.},
volume = {44},
number = {1},
month = apr,
year = {2017},
}

The Preconditioners software contained herein is copyright (C) 2016-2022 by David M. Rosen, and is distributed under the terms of the GNU Lesser General Public License (LGPL) version 3 (or later). Please see the LICENSE for more information.

The modified version of the sym-ildl library redistributed with this project is released under the MIT license. Please refer to the license file distributed with that project.

Contact: [email protected]