An Inverse Iteration Method for Eigenvalue Problems with Eigenvector Nonlinearities

@article{Jarlebring2014AnII,
  title={An Inverse Iteration Method for Eigenvalue Problems with Eigenvector Nonlinearities},
  author={Elias Jarlebring and Simen Kvaal and Wim Michiels},
  journal={ArXiv},
  year={2014},
  volume={abs/1212.0417}
}
Consider a symmetric matrix $A(v)\in\RR^{n\times n}$ depending on a vector $v\in\RR^n$ and satisfying the property $A(\alpha v)=A(v)$ for any $\alpha\in\RR\backslash{0}$. We will here study the problem of finding $(\lambda,v)\in\RR\times \RR^n\backslash\{0\}$ such that $(\lambda,v)$ is an eigenpair of the matrix $A(v)$ and we propose a generalization of inverse iteration for eigenvalue problems with this type of eigenvector nonlinearity. The convergence of the proposed method is studied and… 
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