Optimal expansion of subspaces for eigenvector approximations

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We consider the problem of how to expand a given subspace for approximating an eigenvalue and eigenvector of a matrix A. Specifically, we consider which vector in the subspace, after multiplied by A, provides optimal expansion of the existing subspace for the eigenvalue problem. We determine the optimal vector, when the quality of subspace for approximation is measured by the angle between the subspace and the eigenvector. We have also derived some characterization of the angle that might lead to more practically useful choice of the expansion vector.

Original languageEnglish
Pages (from-to)911-918
Number of pages8
JournalLinear Algebra and Its Applications
Issue number4
StatePublished - Feb 1 2008

Bibliographical note

Funding Information:
1 Supported in part by the National Science Foundation under Grant DMS-0411502.


  • Eigenvector approximations
  • Projection methods
  • Subspace expansion

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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