A Subspace Iteration for Calculating a Cluster of Exterior Eigenvalues

• 作者: Achiya Dax
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: EXTERIOR EIGENVALUES Symmetric MATRICES SUBSPACE ITERATIONS INTERLACING Restarted Krylov Methods
• 年，卷（期）: 2015,（3）
• 页码范围: 76-89
• 页数: 14页
• 分类号: O1

摘要

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.