@Article{EAJAM-7-799,
author = {Kouhei Ooi, Yoshinori Mizuno, Tomohiro Sogabe, Yusaku Yamamoto and Shao-Liang Zhang},
title = {Solution of a Nonlinear Eigenvalue Problem Using Signed Singular Values},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {7},
number = {4},
pages = {799--809},
abstract = {<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>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.181016.300517c},
url = {http://global-sci.org/intro/article_detail/eajam/10721.html}
}