A projection method for nonlinear eigenvalue problems using contour integrals

• Yokota Shinnosuke

  College of Information Science, University of Tsukuba

• Sakurai Tetsuya

  Department of Computer Science, University of Tsukuba CREST, Japan Science and Technology Agency

Abstract

In this paper, we indicate that the Sakurai-Sugiura method with Rayleigh-Ritz projection technique, a numerical method for generalized eigenvalue problems, can be extended to nonlinear eigenvalue problems. The target equation is $T(\lambda)\bm{v}=0$, where $T$ is a matrix-valued function. The method can extract only the eigenvalues within a Jordan curve $\Gamma$ by converting the original problem to a problem with a smaller dimension. Theoretical validation of the method is discussed, and we describe its application using numerical examples.

Journal

• JSIAM Letters

  JSIAM Letters 5 (0), 41-44, 2013

  The Japan Society for Industrial and Applied Mathematics

Keywords

• nonlinear eigenvalue problem
• contour integral
• Rayleigh--Ritz procedure

Details

• CRID: 1390001205299995136
• NII Article ID: 130003371120
• DOI: 10.14495/jsiaml.5.41
• ISSN: 18830617
• ISSN: 18830609
• ISSN: http://id.crossref.org/issn/18830609
• Web Site: https://www.jstage.jst.go.jp/article/jsiaml/5/0/5_41/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed