A Rational Krylov Method Based on Hermite Interpolation for Nonlinear Eigenvalue Problems

@article{Beeumen2013ARK,
  title={A Rational Krylov Method Based on Hermite Interpolation for Nonlinear Eigenvalue Problems},
  author={Roel Van Beeumen and Karl Meerbergen and Wim Michiels},
  journal={SIAM J. Scientific Computing},
  year={2013},
  volume={35}
}
We present a new rational Krylov method for solving the nonlinear eigenvalue problem (NLEP) A(λ)x = 0. The method approximates A(λ) by Hermite interpolation where the degree of the interpolating polynomial and the interpolation points are not fixed in advance. It uses a companion-type reformulation to obtain a linear generalized eigenvalue problem (GEP). This GEP is solved by a rational Krylov method that preserves the structure. As a result, the companion form grows in each iteration and the… CONTINUE READING
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