Bart Vandereycken

Robust Rayleigh quotient minimization and nonlinear eigenvalue problems

by , ,

Abstract:

We present a theoretical framework for studying the robust Rayleigh quotient optimization problem by exploiting its characterization as a nonlinear eigenvalue problem with eigenvector nonlinearity. Our analysis reveals that a commonly used iterative method can be divergent due to a wrong ordering of the eigenvalues of the corresponding nonlinear eigenvalue problem. Two strategies are proposed to address this issue: a spectral transformation based on nonlinear shifting and using second-order derivatives. Numerical experiments for applications in generalized eigenvalue classification and common spatial analysis demonstrate the effectiveness of our proposed approaches.

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Reference:

Z. Bai, D. Lu, B. Vandereycken, "Robust Rayleigh quotient minimization and nonlinear eigenvalue problems", In SIAM J. Sci. Comput., vol. 40, no. 5, pp. A3495-A3522, 2018.

Bibtex Entry:

@article{Bai_LV:2018,
	Abstract = {We present a theoretical framework for studying the robust Rayleigh quotient optimization problem by exploiting its characterization as a nonlinear eigenvalue problem with eigenvector nonlinearity. Our analysis reveals that a commonly used iterative method can be divergent due to a wrong ordering of the eigenvalues of the corresponding nonlinear eigenvalue problem. Two strategies are proposed to address this issue: a spectral transformation based on nonlinear shifting and using second-order derivatives. Numerical experiments for applications in generalized eigenvalue classification and common spatial analysis demonstrate the effectiveness of our proposed approaches.},
    Author = {Bai, Z. and Lu, D. and Vandereycken, B.},
    Journal = {SIAM J. Sci. Comput.},
    Number = {5},
    Pages = {A3495--A3522},
    Title = {Robust Rayleigh quotient minimization and nonlinear eigenvalue problems},
    Volume = {40},
    Year = {2018},
    Pdf = {http://www.unige.ch/math/vandereycken/papers/published_Bai_LV_2018.pdf},
    Doi = {10.1137/18M1167681}
}