ALAMT  Vol.5 No.3 , September 2015
A Subspace Iteration for Calculating a Cluster of Exterior Eigenvalues
Author(s) Achiya Dax*
ABSTRACT
In this paper we present a new subspace iteration for calculating eigenvalues of symmetric matrices. The method is designed to compute a cluster of k exterior eigenvalues. For example, k eigenvalues with the largest absolute values, the k algebraically largest eigenvalues, or the k algebraically smallest eigenvalues. The new iteration applies a Restarted Krylov method to collect information on the desired cluster. It is shown that the estimated eigenvalues proceed monotonically toward their limits. Another innovation regards the choice of starting points for the Krylov subspaces, which leads to fast rate of convergence. Numerical experiments illustrate the viability of the proposed ideas.

Cite this paper
Dax, A. (2015) A Subspace Iteration for Calculating a Cluster of Exterior Eigenvalues. Advances in Linear Algebra & Matrix Theory, 5, 76-89. doi: 10.4236/alamt.2015.53008.
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