hlib

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 26 articles , 1 standard article )

Showing results 1 to 20 of 26.
Sorted by year (citations)

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  1. Börm, Steffen; Christophersen, Sven: Approximation of integral operators by Green quadrature and nested cross approximation (2016)
  2. Hackbusch, Wolfgang: Survey on the technique of hierarchical matrices (2016)
  3. Hao, Sijia; Martinsson, Per-Gunnar: A direct solver for elliptic PDEs in three dimensions based on hierarchical merging of Poincaré-Steklov operators (2016)
  4. Martinsson, Per-Gunnar: Compressing rank-structured matrices via randomized sampling (2016)
  5. Pan, Victor Y.: How bad are Vandermonde matrices? (2016)
  6. Sushnikova, Darya A.; Oseledets, Ivan V.: Preconditioners for hierarchical matrices based on their extended sparse form (2016)
  7. Corona, Eduardo; Martinsson, Per-Gunnar; Zorin, Denis: An $O(N)$ direct solver for integral equations on the plane (2015)
  8. Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk: $\mathcal H$-matrix approximability of the inverses of FEM matrices (2015)
  9. Gillman, Adrianna; Barnett, Alex H.; Martinsson, Per-Gunnar: A spectrally accurate direct solution technique for frequency-domain scattering problems with variable media (2015)
  10. Pan, Victor Y.: Transformations of matrix structures work again (2015)
  11. Xia, Jianlin; Xi, Yuanzhe; Cauley, Stephen; Balakrishnan, Venkataramanan: Fast sparse selected inversion (2015)
  12. Börm, Steffen; Gördes, Jessica: Low-rank approximation of integral operators by using the Green formula and quadrature (2013)
  13. Roman, J.E.; Vasconcelos, P.B.; Nunes, A.L.: Eigenvalue computations in the context of data-sparse approximations of integral operators (2013)
  14. Zechner, Jürgen; Beer, Gernot: A fast elasto-plastic formulation with hierarchical matrices and the boundary element method (2013)
  15. Benner, Peter; Mach, Thomas: Computing all or some eigenvalues of symmetric $\calH_\ell$-matrices (2012)
  16. Gillman, Adrianna; Young, Patrick M.; Martinsson, Per-Gunnar: A direct solver with $O(N)$ complexity for integral equations on one-dimensional domains (2012)
  17. Ullmann, Elisabeth; Elman, Howard C.; Ernst, Oliver G.: Efficient iterative solvers for stochastic Galerkin discretizations of log-transformed random diffusion problems (2012)
  18. Benner, Peter; Mach, Thomas: On the QR decomposition of $\mathcal H$-matrices (2010)
  19. Börm, Steffen: Efficient numerical methods for non-local operators. $\cal H^2$-matrix compression, algorithms and analysis. (2010)
  20. Khoromskij, B.N.; Litvinenko, A.; Matthies, H.G.: Application of hierarchical matrices for computing the Karhunen-Loève expansion (2009)

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