Filter analysis for the stochastic estimation of eigenvalue counts

• Maeda Yasuyuki

  Department of Computer Science, University of Tsukuba

• Futamura Yasunori

  Department of Computer Science, University of Tsukuba Ph.D. Program in Life Science Innovation, University of Tsukuba

• Imakura Akira

  Department of Computer Science, University of Tsukuba

• Sakurai Tetsuya

  Department of Computer Science, University of Tsukuba CREST, Japan Science and Technology Agency Ph.D. Program in Life Science Innovation, University of Tsukuba

Abstract

To estimate the number of eigenvalues of a Hermitian matrix that are located in a given interval, existing methods include polynomial filtering and rational filtering. Both filtering approaches are based on stochastic approximations for matrix trace. In this paper, we analyze a rational filtering method that is based on polynomial filtering in which the solutions to the linear systems are approximated by a Krylov subspace method. Our analysis and numerical experiments indicate that the rational filtering method is effective when the eigenvalues of a given matrix are sparsely distributed in the target interval.

Journal

• JSIAM Letters

  JSIAM Letters 7 (0), 53-56, 2015

  The Japan Society for Industrial and Applied Mathematics

Keywords

• eigenvalue counts
• stochastic estimation
• Krylov subspace methods

Details

• CRID: 1390001205300276864
• NII Article ID: 130005087644
• DOI: 10.14495/jsiaml.7.53
• ISSN: 18830617
• ISSN: 18830609
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed