README.md

June 18, 2025 · View on GitHub

$\mathcal{H}-Matrices$

Curated list of Hierarchical Matrices ( $\mathcal{H}$ -Matrices) libraries (by language) and papers (by year). Inspired by the awesome-awesomeness list.

C

HiCMA Hatem Ltaief, Kadir Akbudak (King Abdullah University of Science and Technology)

Open source
Hierarchical format: $\mathcal{H}$

Hlib Lars Grasedyck and Steffen Börm (Leipzig, Max Planck Institute)

Source code available through signed license agreement.
Hierarchical format: $\mathcal{H}$ and $\mathcal{H}^2$

H2Lib Steffen Boerm, Knut Reimer, Dirk Boysen, Sven Christophersen, Nadine Albrecht, and Jens Burmeister. (University of Kiel)

Open source
Hierarchical format: $\mathcal{H}$ and $\mathcal{H}^2$

H2Pack Hua Huang, Xin Xing, and Edmond Chow (Georgia Tech)

Open source (MIT license)
Hierarchical format: $\mathcal{H}^2$ , HSS

C++

HLIBpro Ronald Kriemann (Leipzig, Max Planck Institute)

Binary files only, distributed memory implementation on MPI, on shared memory based on TBB
Hierarchical format: $\mathcal{H}$ and $\mathcal{H}^2$

AHMED Mario Bebendorf and Sergej Rjasanow (University of Bonn)

Source code available through online license agreement.
Hierarchical format: $\mathcal{H}$

BBFMM3D W. Fong, and E. Darve (Stanford University)

Black-box fast multipole method for general kernels. The FMM is based on Chebyshev and Fourier interpolation methods.

BEM++ W. Smigaj, S. Arridge, T. Betcke, J. Phillips, M. Schweiger (University College London)

Boundary Integral Problems with BEM++, accelerated by $\mathcal{H}$ -Matrices

DMHM Jack Poulson and Ryan Li (Stanford University and Georgia Tech)

Open source
Hierarchical format: $\mathcal{H}$

STRUMPACK X. Sherry Li, Pieter Ghysels, Gustavo Chávez, Yang Liu (Lawrence Berkeley National Laboratory)

Open source
Hierarchical format: HSS, HOLDR, BLR

Dense_HODLR Amirhossein Aminfar (Stanford University)

Open source
Hierarchical format: HODLR

Structured CHOLMOD David Bindel (Cornell University)

Open source

LoRaSp Hadi Pouransari and Eric Darve (Stanford University)

Hierarchical format: $\mathcal{H}^2$
A revised version of LORASP with additional options and a more modular software design

RLCM Jie Chen (IBM)

linear complexity assembly
sub-linear complexity solves: $O(n)$ many solves in $O(n \log(n))$ complexity

CUDA

hmglib Peter Zaspel (University of Basel)

Open source
Hierarchical format: $\mathcal{H}$

Matlab

Misc Per-Gunnar Martinsson (University of Colorado Boulder)

Various scripts, Randomized SVD, Interpolative decomposition, Multi-frontal solvers.
Hierarchical format: S, HSS

HSS Jianlin Xia (Purdue University)

Hierarchically SemiSeparable package
Hierarchical format: HSS

RSVDPACK Sergey Voronin and Per-Gunnar Martinsson (University of Colorado Boulder)

Randomized SVD on GPU
C and Matlab codes

HMat Haizhao Yang and Yingzhou Li (Duke University and Stanford University)

Hierarchical Matrices in Julia and Matlab
Matlab library for many types of structured matrices

Fortran

SSS_Toeplitz Jianlin Xia and J. Zhu (Purdue University)

Superfast SSS Toeplitz solver
Hierarchical format: HSS

HACApK Akihiro Ida (The University of Tokyo)

Lattice H-matrices
Hierarchical format: $\mathcal{H}$

Python

H2Tools Alexander Mikhalev (KAUST / Russian Academy of Sciences)

Open source
Hierarchical format: $\mathcal{H}^2$

Julia

KernelMatrices.jl Chris Geoga (Argonne National Laboratory)

HODLR matrices with ACA or Nystrom approximation for off-diagonal blocks
First and second derivatives of kernel matrices that are continuous with respect to kernel parameters

HssMatrices.jl Boris Bonev (EPFL)

library for HSS matrices in Julia
various compression algorithms, fast solvers and multiplication, as well as visualization tools

HMatrices.jl Luiz M. Faria (INRIA)

$\mathcal{H}$ hierarchical format with support for $\mathcal{H}$ -LU factorization
Focus on applications to boundary integral equation methods

Woud you like to add a new library or update a link?

Please open a pull request, contributions to this repository are most welcome.