A Subspace Method for Large-Scale Eigenvalue Optimization

@article{Kangal2018ASM,
  title={A Subspace Method for Large-Scale Eigenvalue Optimization},
  author={Fatih Kangal and Karl Meerbergen and Emre Mengi and Wim Michiels},
  journal={SIAM J. Matrix Analysis Applications},
  year={2018},
  volume={39},
  pages={48-82}
}
We consider the minimization or maximization of the Jth largest eigenvalue of an analytic and Hermitian matrix-valued function, and build on Mengi et al. (2014, SIAM J. Matrix Anal. Appl., 35, 699-724). This work addresses the setting when the matrix-valued function involved is very large. We describe subspace procedures that convert the original problem into a small-scale one by means of orthogonal projections and restrictions to certain subspaces, and that gradually expand these subspaces… CONTINUE READING

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