Computing and Visualization in Science

, Volume 16, Issue 6, pp 271–282 | Cite as

Computing the eigenvalues of symmetric \({\fancyscript{H}}^2\)-matrices by slicing the spectrum

  • Peter Benner
  • Steffen BörmEmail author
  • Thomas Mach
  • Knut Reimer


The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade (Knyazev et al. in Numerical solution of PDE eigenvalue problems, vol 56. Mathematisches Forschungsinstitut, Oberwolfach, 2013). Here we present an new algorithm based on slicing the spectrum that takes advantage of the rank structure of resolvent matrices in order to compute \(m\) eigenvalues of the generalized symmetric eigenvalue problem in \({\fancyscript{O}}(nm\log ^\alpha n)\) operations, where \(\alpha >0\) is a small constant.


\({\fancyscript{H}}^2\)-matrices Symmetric generalized eigenproblem Slicing the spectrum 

Mathematics Subject Classification

65F15 65F50 15A18 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Peter Benner
    • 1
  • Steffen Börm
    • 2
    Email author
  • Thomas Mach
    • 3
  • Knut Reimer
    • 2
  1. 1.Max Planck Institute for Dynamics of Complex Technical SystemsMagdeburgGermany
  2. 2.Institut für InformatikUniversität KielKielGermany
  3. 3.Department of Computer ScienceKU LeuvenHeverlee, LeuvenBelgium

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