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A Newton-like method for computing deflating subspaces
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DOI：10.1515/jnma-2015-0019.png)
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Abstract
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This work is devoted to computations of deflating subspaces associated with separated groups of finite eigenvalues near specified shifts of large regular matrix pencils. The proposed method is a combination of inexact inverse subspace iteration and Newton's method. The first one is slow but reliably convergent starting with almost an arbitrary initial subspace and it is used as a preprocessing to obtain a good initial guess for the second method which is fast but only locally convergent. The Newton method necessitates at each iteration the solution of a generalized Sylvester equation and for this task an iterative algorithm based on the preconditioned GMRES method is devised. Numerical properties of the proposed combination are illustrated with a typical hydrodynamic stability problem.
Keywords:
Newton's method
inverse subspace iteration
regular matrix pencil
finite eigenvalues
deflating subspaces
generalized Sylvester equation
GMRES
preconditioning
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