A new method for computing the stable invariant subspace of a real Hamiltonian matrix (1997)
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@MISC{Benner97anew,
author = {Peter Benner and Volker Mehrmann and Hongguo Xu},
title = {A new method for computing the stable invariant subspace of a real Hamiltonian matrix},
year = {1997}
}
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Abstract
A new backward stable, structure preserving method of complexity O(n 3 ) is presented for computing the stable invariant subspace of a real Hamiltonian matrix and the stabilizing solution of the continuous-time algebraic Riccati equation. The new method is based on the relationship between the invariant subspaces of the Hamiltonian matrix H and the extended matrix 0 H H 0 and makes use of the symplectic URV-like decomposition that was recently introduced by the authors. Keywords. Eigenvalue problem, Hamiltonian matrix, algebraic Riccati equation, sign function, invariant subspace. AMS subject classification. 65F15, 93B40, 93B36, 93C60. 1 Introduction It is a well accepted fact in numerical analysis that a numerical algorithm should reflect as many of the structural properties of the physical problem or the resulting mathematical model. For the solution of eigenvalue problems this means that use of the symmetry structures of the matrix or the spectrum is made. While for symme...
