, Volume 81, Issue 4, pp 259–268 | Cite as

A projection method for the computation of inner eigenvalues using high degree rational operators

  • W. HackbuschEmail author
  • W. Kress


To efficiently calculate only part of the spectrum of a matrix, one can use a projection onto a suitable subspace. In this work, we present a technique to efficiently calculate such a projection without knowledge of the spectrum. The technique requires only few matrix–matrix products and inversions, which for some classes of matrices, like the \({\mathcal{H}}\) -matrices, can be computed in almost linear complexity.


eigenvalue computation spectral projection sign function high-degree polynomials 

AMS Subject Classifications

65N25 65F15 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

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