Year: 2017
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.181016.300517c
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 4 : pp. 799–809
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Nonlinear eigenvalue problem signed singular value scaling exponent turbulent flow.