Volume 7, Issue 4
Solution of a Nonlinear Eigenvalue Problem Using Signed Singular Values

East Asian J. Appl. Math., 7 (2017), pp. 799-809.

Published online: 2018-02

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• Abstract

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.

• Keywords

Nonlinear eigenvalue problem, signed singular value, scaling exponent, turbulent flow.

15A18, 47J10, 65F15

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@Article{EAJAM-7-799, author = {}, 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 = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.181016.300517c}, url = {http://global-sci.org/intro/article_detail/eajam/10721.html} }
TY - JOUR T1 - Solution of a Nonlinear Eigenvalue Problem Using Signed Singular Values 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 -

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.

Kouhei Ooi, Yoshinori Mizuno, Tomohiro Sogabe, Yusaku Yamamoto & Shao-Liang Zhang. (2020). Solution of a Nonlinear Eigenvalue Problem Using Signed Singular Values. East Asian Journal on Applied Mathematics. 7 (4). 799-809. doi:10.4208/eajam.181016.300517c
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