A Subspace Iteration for Calculating a Cluster of Exterior Eigenvalues

Achiya  Dax

doi:10.4236/alamt.2015.53008

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.

Keywords: Exterior Eigenvalues, Symmetric Matrices, Subspace Iterations, Interlacing, Restarted Krylov Methods

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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