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Solution of a Nonlinear Eigenvalue Problem Using Signed Singular Values

  • Kouhei Ooi (a1), Yoshinori Mizuno (a2), Tomohiro Sogabe (a1), Yusaku Yamamoto (a3) and Shao-Liang Zhang (a1)...
Abstract

We propose a robust numerical algorithm for solving the nonlinear eigenvalue problem A(ƛ)x = 0. Our algorithm is based on the idea of finding the value of ƛ for which A(ƛ) is singular by computing the smallest eigenvalue or singular value of A(ƛ) viewed as a constant matrix. To further enhance computational efficiency, we introduce and use the concept of signed singular value. Our method is applicable when A(ƛ) is large and nonsymmetric and has strong nonlinearity. Numerical experiments on a nonlinear eigenvalue problem arising in the computation of scaling exponent in turbulent flow show robustness and effectiveness of our method.

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*Corresponding author. Email address:yusaku.yamamoto@uec.ac.jp (Y. Yamamoto)
References
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East Asian Journal on Applied Mathematics
  • ISSN: 2079-7362
  • EISSN: 2079-7370
  • URL: /core/journals/east-asian-journal-on-applied-mathematics
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