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 44 articles , 1 standard article )

Showing results 1 to 20 of 44.
Sorted by year (citations)

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  1. Börm, Steffen: Adaptive compression of large vectors (2018)
  2. Xing, Xin; Chow, Edmond: Preserving positive definiteness in hierarchically semiseparable matrix approximations (2018)
  3. Betcke, Timo; van’t Wout, Elwin; Gélat, Pierre: Computationally efficient boundary element methods for high-frequency Helmholtz problems in unbounded domains (2017)
  4. Corona, Eduardo; Rahimian, Abtin; Zorin, Denis: A tensor-train accelerated solver for integral equations in complex geometries (2017)
  5. Dölz, J.; Harbrecht, H.; Peters, M. D.: $\mathcalH$-matrix based second moment analysis for rough random fields and finite element discretizations (2017)
  6. Dölz, J.; Harbrecht, H.; Schwab, Ch.: Covariance regularity and $\mathcal H$-matrix approximation for rough random fields (2017)
  7. Pan, Victor Y.: Fast approximate computations with Cauchy matrices and polynomials (2017)
  8. Vasconcelos, Paulo B.: Data-sparse approximation on the computation of a weakly singular Fredholm equation: a stellar radiative transfer application (2017)
  9. Ballani, Jonas; Kressner, Daniel: Matrices with hierarchical low-rank structures (2016)
  10. Börm, Steffen; Christophersen, Sven: Approximation of integral operators by Green quadrature and nested cross approximation (2016)
  11. Falletta, Silvia; Sauter, Stefan A.: The panel-clustering method for the wave equation in two spatial dimensions (2016)
  12. Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk: Existence of $\mathcalH$-matrix approximants to the inverses of BEM matrices: the simple-layer operator (2016)
  13. Hackbusch, Wolfgang: Survey on the technique of hierarchical matrices (2016)
  14. Hao, Sijia; Martinsson, Per-Gunnar: A direct solver for elliptic PDEs in three dimensions based on hierarchical merging of Poincaré-Steklov operators (2016)
  15. Martinsson, Per-Gunnar: Compressing rank-structured matrices via randomized sampling (2016)
  16. Mikhalev, A. Yu.; Oseledets, I. V.: Iterative representing set selection for nested cross approximation. (2016)
  17. Pan, Victor Y.: How bad are Vandermonde matrices? (2016)
  18. Pan, Victor Y.; Zhao, Liang: Low-rank approximation of a matrix: novel insights, new progress, and extensions (2016)
  19. Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter; Napov, Artem: A distributed-memory package for dense hierarchically semi-separable matrix computations using randomization (2016)
  20. Sushnikova, Darya A.; Oseledets, Ivan V.: Preconditioners for hierarchical matrices based on their extended sparse form (2016)

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