HLib is a library for hierarchical matrices that was written by Lars Grasedyck and Steffen Börm. Most routines are written in the C programming language using BLAS and LAPACK for lower-level algebraic operations. The library contains functions for H- and H2-matrix arithmetics, the treatment of partial differential equations and a number of integral operators as well as support routines for the creation of cluster trees, visualization and numerical quadrature. This is a work in progress, so there may be undiscovered errors and you can expect new features to appear with every new release.

References in zbMATH (referenced in 70 articles , 1 standard article )

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  1. Eshghi, Nasim; Mach, Thomas; Reichel, Lothar: New matrix function approximations and quadrature rules based on the Arnoldi process (2021)
  2. Schäfer, Florian; Sullivan, T. J.; Owhadi, Houman: Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity (2021)
  3. Steinbach, Olaf; Zank, Marco: A note on the efficient evaluation of a modified Hilbert transformation (2021)
  4. Zhang, Yabin; Gillman, Adrianna: A fast direct solver for two dimensional quasi-periodic multilayered media scattering problems (2021)
  5. Ayala, Alan; Claeys, Xavier; Grigori, Laura: Linear-time CUR approximation of BEM matrices (2020)
  6. Börm, Steffen; Börst, Christina: Hybrid matrix compression for high-frequency problems (2020)
  7. Dölz, Jürgen: A higher order perturbation approach for electromagnetic scattering problems on random domains (2020)
  8. Keßler, Torsten; Rjasanow, Sergej; Weißer, Steffen: Vlasov-Poisson system tackled by particle simulation utilizing boundary element methods (2020)
  9. Massei, Stefano; Robol, Leonardo; Kressner, Daniel: Hm-toolbox: MATLAB software for HODLR and HSS matrices (2020)
  10. Sushnikova, Daria A.; Oseledets, Ivan V.: Simple non-extensive sparsification of the hierarchical matrices (2020)
  11. Alger, Nick; Rao, Vishwas; Myers, Aaron; Bui-Thanh, Tan; Ghattas, Omar: Scalable Matrix-free adaptive product-convolution approximation for locally translation-invariant operators (2019)
  12. Betcke, Timo; Haberl, Alexander; Praetorius, Dirk: Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra (2019)
  13. Boukaram, Wajih; Turkiyyah, George; Keyes, David: Randomized GPU algorithms for the construction of hierarchical matrices from matrix-vector operations (2019)
  14. Chen, Duan; Cai, Wei: An (O(N \logN)) hierarchical random compression method for kernel matrices by sampling partial matrix entries (2019)
  15. Dölz, Jürgen; Harbrecht, Helmut; Multerer, Michael D.: On the best approximation of the hierarchical matrix product (2019)
  16. Dölz, Jürgen; Kurz, Stefan; Schöps, Sebastian; Wolf, Felix: Isogeometric boundary elements in electromagnetism: rigorous analysis, fast methods, and examples (2019)
  17. Karkulik, Michael; Melenk, Jens Markus: (\mathscrH)-matrix approximability of inverses of discretizations of the fractional Laplacian (2019)
  18. Kressner, Daniel; Massei, Stefano; Robol, Leonardo: Low-rank updates and a divide-and-conquer method for linear matrix equations (2019)
  19. Shepherd, David; Miles, James; Heil, Matthias; Mihajlović, Milan: An adaptive step implicit midpoint rule for the time integration of Newton’s linearisations of non-linear problems with applications in micromagnetics (2019)
  20. Börm, Steffen: Adaptive compression of large vectors (2018)

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Further publications can be found at: http://www.hmatrix.org/literature.html