Simple non-extensive sparsification of the hierarchical matrices

Daria A. Sushnikova*, Ivan V. Oseledets

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we consider the matrices approximated in H 2 format. The direct solution, as well as the preconditioning of systems with such matrices, is a challenging problem. We propose a non-extensive sparse factorization of the H 2 matrix that allows to substitute direct H 2 solution with the solution of the system with an equivalent sparse matrix of the same size. The sparse factorization is constructed of parameters of the H 2 matrix. In the numerical experiments, we show the consistency of this approach in comparison with the other approximate block low-rank hierarchical solvers, such as HODLR [3], H2Lib [5], and IFMM [11].

Original languageEnglish (US)
Article number52
JournalAdvances in Computational Mathematics
Issue number4
StatePublished - Jul 1 2020

Bibliographical note

Funding Information:
Section 2 is supported by Russian Foundation for Basic Research grant 17-01-00854, Sections 3 and 4 are supported by Russian Foundation for Basic Research grant 16-31-60095, Sectiom 5 is supported by Russian Science Foundation grant 15-11-00033.

Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.


  • H matrix
  • Preconditioning
  • Sparse factorization

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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