An Eigendecomposition Tracking Method for Real Symmetric Matrices Based on Ogita-Aishima's Eigenvector Refinement Algorithm

Abstract

Abstract. We propose a method to track the eigendecomposition of a time-dependent real symmetric matrix A(t) using Ogita-Aishima’s eigenvector refinement algorithm. In the tracking, the difference between the eigenpairs of A(t) and those of A(t + Δt) can become large depending on Δt. Also, convergence of the Ogita-Aishima algorithm deteriorates when multiple eigenvalues cross each other. In this paper, we improve Ogita-Aishima’s convergence theorem to enlarge the convergence radius and also propose a preprocessing method that improves the convergence property.