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 63 articles , 1 standard article )

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  1. Ayala, Alan; Claeys, Xavier; Grigori, Laura: Linear-time CUR approximation of BEM matrices (2020)
  2. Dölz, Jürgen: A higher order perturbation approach for electromagnetic scattering problems on random domains (2020)
  3. Keßler, Torsten; Rjasanow, Sergej; Weißer, Steffen: Vlasov-Poisson system tackled by particle simulation utilizing boundary element methods (2020)
  4. Massei, Stefano; Robol, Leonardo; Kressner, Daniel: Hm-toolbox: MATLAB software for HODLR and HSS matrices (2020)
  5. Sushnikova, Daria A.; Oseledets, Ivan V.: Simple non-extensive sparsification of the hierarchical matrices (2020)
  6. Alger, Nick; Rao, Vishwas; Myers, Aaron; Bui-Thanh, Tan; Ghattas, Omar: Scalable Matrix-free adaptive product-convolution approximation for locally translation-invariant operators (2019)
  7. Boukaram, Wajih; Turkiyyah, George; Keyes, David: Randomized GPU algorithms for the construction of hierarchical matrices from matrix-vector operations (2019)
  8. Dölz, Jürgen; Harbrecht, Helmut; Multerer, Michael D.: On the best approximation of the hierarchical matrix product (2019)
  9. Dölz, Jürgen; Kurz, Stefan; Schöps, Sebastian; Wolf, Felix: Isogeometric boundary elements in electromagnetism: rigorous analysis, fast methods, and examples (2019)
  10. Karkulik, Michael; Melenk, Jens Markus: (\mathscrH)-matrix approximability of inverses of discretizations of the fractional Laplacian (2019)
  11. Kressner, Daniel; Massei, Stefano; Robol, Leonardo: Low-rank updates and a divide-and-conquer method for linear matrix equations (2019)
  12. 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)
  13. Börm, Steffen: Adaptive compression of large vectors (2018)
  14. Dölz, Jürgen; Harbrecht, Helmut: Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains (2018)
  15. Feischl, Michael; Kuo, Frances Y.; Sloan, Ian H.: Fast random field generation with (H)-matrices (2018)
  16. Xing, Xin; Chow, Edmond: Preserving positive definiteness in hierarchically semiseparable matrix approximations (2018)
  17. Betcke, Timo; van’t Wout, Elwin; Gélat, Pierre: Computationally efficient boundary element methods for high-frequency Helmholtz problems in unbounded domains (2017)
  18. Börm, Steffen; Melenk, Jens M.: Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis (2017)
  19. Chávez, Gustavo; Turkiyyah, George; Keyes, David E.: A direct elliptic solver based on hierarchically low-rank Schur complements (2017)
  20. Corona, Eduardo; Rahimian, Abtin; Zorin, Denis: A tensor-train accelerated solver for integral equations in complex geometries (2017)

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