A numerical method for nonlinear eigenvalue problems using contour integrals
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TL;DR: A contour integral method is proposed to solve nonlinear eigenvalue problems numerically by reducing the original problem to a linear eigen value problem that has identical eigenvalues in the domain.
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Abstract: A contour integral method is proposed to solve nonlinear eigenvalue problems numerically. The target equation is F (λ)x = 0, where the matrix F (λ) is an analytic matrix function of λ. The method can extract only the eigenvalues λ in a domain defined by the integral path, by reducing the original problem to a linear eigenvalue problem that has identical eigenvalues in the domain. Theoretical aspects of the method are discussed, and we illustrate how to apply of the method with some numerical examples.
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Elias Jarlebring
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Subspace projection methods for model order reduction and nonlinear eigenvalue computation
Zhaojun Bai,Ben-Shan Liao +1 more
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TL;DR: In this paper, the authors present a coupling-matrix based subspace projection algorithm for the component mode synthesis (CMS) method, referred to as the CMSχ method, which is compatible with the one in recently proposed optimal modal reduction (OMR) method.
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