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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
55/2007

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

Wolfgang Hackbusch and Wendy Kress

Abstract

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.

Received:
Jun 8, 2007
Published:
Jun 8, 2007
Keywords:
eigenvalue computation

Related publications

inJournal
2007 Repository Open Access
Wolfgang Hackbusch and Wendy Kress

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

In: Computing, 81 (2007) 4, pp. 259-268