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

• Shiroma Kurumi

  Faculty of Informatics and Engineering The University of Electro-Communications

• Kudo Shuhei

  Faculty of Informatics and Engineering The University of Electro-Communications

• Yamamoto Yusaku

  Faculty of Informatics and Engineering The University of Electro-Communications

Bibliographic Information

Other Title

• 荻田・相島の固有ベクトル反復改良法に基づく実対称行列の固有値分解追跡手法

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.

Journal

• Transactions of the Japan Society for Industrial and Applied Mathematics

  Transactions of the Japan Society for Industrial and Applied Mathematics 29 (1), 78-120, 2019

  The Japan Society for Industrial and Applied Mathematics

Keywords

• 時間依存固有値問題
• 反復解法
• 収束性解析
• 高性能計算

Details

• CRID: 1390282763117655936
• NII Article ID: 130007618979
• DOI: 10.11540/jsiamt.29.1_78
• ISSN: 24240982
• Text Lang: ja
• Data Source:
  • JaLC
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed