Iterative representing set selection for nested cross approximation

A. Yu Mikhalev, I. V. Oseledets

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Summary: A new fast algebraic method for obtaining an -approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum volume principle to select submatrices in low-rank matrices. A special iterative approach for the computation of so-called representing sets is established. The main advantage of the method is that it uses only the hierarchical partitioning of the matrix and does not require special 'proxy surfaces' to be selected in advance. The numerical experiments for the electrostatic problem and for the boundary integral operator confirm the effectiveness and robustness of the approach. The complexity is linear in the matrix size and polynomial in the ranks. The algorithm is implemented as an open-source Python package that is available online. Copyright

Original languageEnglish
Pages (from-to)230-248
Number of pages19
JournalNumerical Linear Algebra with Applications
Volume23
Issue number2
DOIs
Publication statusPublished - 1 Mar 2016
Externally publishedYes

Keywords

  • Cross approximation
  • Hiearchical matrices
  • Low-rank approximation
  • Skeleton decomposition

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