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 75 articles , 1 standard article )

Showing results 61 to 75 of 75.
Sorted by year (citations)
  1. Roman, J. E.; Vasconcelos, P. B.; Nunes, A. L.: Eigenvalue computations in the context of data-sparse approximations of integral operators (2013)
  2. Zechner, Jürgen; Beer, Gernot: A fast elasto-plastic formulation with hierarchical matrices and the boundary element method (2013)
  3. Benner, Peter; Mach, Thomas: Computing all or some eigenvalues of symmetric (\mathcalH_\ell)-matrices (2012)
  4. Gillman, Adrianna; Young, Patrick M.; Martinsson, Per-Gunnar: A direct solver with (O(N)) complexity for integral equations on one-dimensional domains (2012)
  5. Ullmann, Elisabeth; Elman, Howard C.; Ernst, Oliver G.: Efficient iterative solvers for stochastic Galerkin discretizations of log-transformed random diffusion problems (2012)
  6. Benner, Peter; Mach, Thomas: On the QR decomposition of (\mathcalH)-matrices (2010)
  7. Börm, Steffen: Efficient numerical methods for non-local operators. (\mathcalH^2)-matrix compression, algorithms and analysis. (2010)
  8. Khoromskij, B. N.; Litvinenko, A.; Matthies, H. G.: Application of hierarchical matrices for computing the Karhunen-Loève expansion (2009)
  9. Baur, U.: Low rank solution of data-sparse Sylvester equations (2008)
  10. Zitzmann, Martin L.; Weigel, Robert: Fast and efficient methods for circuit-based automotive EMC simulation (2008)
  11. Le Borne, S.; Cook, D. II: Construction of a discrete divergence-free basis through orthogonal factorization in (\mathcalH)-arithmetic (2007)
  12. Baur, U.; Benner, P.: Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic (2006)
  13. Börm, S.: Approximation of integral operators by (\mathcalH^2)-matrices with adaptive bases (2005)
  14. Börm, Steffen; Grasedyck, Lars: Hybrid cross approximation of integral operators (2005)
  15. Grasedyck, L.: Adaptive recompression of (\mathcalH)-matrices for BEM (2005)

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