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Solution of a Nonlinear Eigenvalue Problem Using Signed Singular Values

Solution of a Nonlinear Eigenvalue Problem Using Signed Singular Values

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.