Continuation of low-dimensional invariant subspaces in dynamical systems of large dimension

@inproceedings{Beyn2005ContinuationOL,
  title={Continuation of low-dimensional invariant subspaces in dynamical systems of large dimension},
  author={Wolf-J{\"u}rgen Beyn and Winfried Kle\ss and Vera Th{\"u}mmler},
  year={2005}
}
We present a continuation method for low-dimensional invariant subspaces of a parameterized family of large and sparse real matrices. Such matrices typically occur when linearizing about branches of steady states in dynamical systems that are obtained by spatial discretization of timedependent PDE’s. The main interest is in subspaces that belong to spectral sets close the imaginary axis. Our continuation procedure provides bases of the invariant subspaces that depend smoothly on the parameter… CONTINUE READING
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