Combinatorial preconditioning for accelerating the convergence of the parallel block Jacobi method for the symmetric eigenvalue problem

• Kugaya Masaki

  The University of Electro-Communications

• Kudo Shuhei

  The University of Electro-Communications

• Yamamoto Yusaku

  The University of Electro-Communications

Abstract

In this paper, we propose combinatorial preconditioning to accelerate the convergence of the parallel block Jacobi method for the symmetric eigenvalue problem. The idea is to gather matrix elements of large modulus near the diagonal prior to each annihilation by permutation of rows and columns and annihilate them at once, thereby leading to large reduction of the off-diagonal norm. Numerical experiments show that the resulting method can actually speedup the convergence and reduce the execution time of the parallel block Jacobi method.

Journal

• JSIAM Letters

  JSIAM Letters 13 (0), 56-59, 2021

  The Japan Society for Industrial and Applied Mathematics

Keywords

• symmetric eigenvalue problem
• block Jacobi method
• preconditioning
• combinatorial optimization
• parallel computing

Details

• CRID: 1390571007536542464
• NII Article ID: 130008092825
• DOI: 10.14495/jsiaml.13.56
• ISSN: 18830617
• ISSN: 18830609
• Web Site: https://www.jstage.jst.go.jp/article/jsiaml/13/0/13_56/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed