Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum

Peter Benner, Steffen Börm, Thomas Mach, Knut Reimer

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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 (Formula presented.) eigenvalues of the generalized symmetric eigenvalue problem in (Formula presented.) operations, where (Formula presented.) is a small constant.

Original languageEnglish
JournalComputing and Visualization in Science
DOIs
Publication statusAccepted/In press - Mar 4 2015
Externally publishedYes

Fingerprint

Slicing
Symmetric matrix
Eigenvalue
Computing
Symmetric Eigenvalue Problem
Generalized Eigenvalue Problem
Finite Element Discretization
Resolvent
Eigenvalue Problem
Numerical Solution

Keywords

  • $${\fancyscript{H}}^2$$H2-matrices
  • Slicing the spectrum
  • Symmetric generalized eigenproblem

ASJC Scopus subject areas

  • Modelling and Simulation
  • Theoretical Computer Science
  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Engineering(all)

Cite this

Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum. / Benner, Peter; Börm, Steffen; Mach, Thomas; Reimer, Knut.

In: Computing and Visualization in Science, 04.03.2015.

Research output: Contribution to journalArticle

Benner, Peter ; Börm, Steffen ; Mach, Thomas ; Reimer, Knut. / Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum. In: Computing and Visualization in Science. 2015.
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