TY - JOUR
T1 - Solution of a Nonlinear Eigenvalue Problem Using Signed Singular Values
AU - Kouhei Ooi, Yoshinori Mizuno, Tomohiro Sogabe, Yusaku Yamamoto & Shao-Liang Zhang
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 799
EP - 809
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.181016.300517c
UR - https://global-sci.org/intro/article_detail/eajam/10721.html
KW - Nonlinear eigenvalue problem, signed singular value, scaling exponent, turbulent flow.
AB - <p style="text-align: justify;">We propose a robust numerical algorithm for solving the nonlinear eigenvalue problem $A(λ)x=0$. Our algorithm is based on the idea of finding the value of $λ$ for which $A(λ)$ is singular by computing the smallest eigenvalue or singular value of $A(λ)$ 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 $A(λ)$ 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.</p>