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A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencilsBenner, P., Mehrmann, V., Xu, H. 30 October 1998 (has links) (PDF)
A new method is presented for the numerical computation of the generalized eigen- values of real Hamiltonian or symplectic pencils and matrices. The method is strongly backward stable, i.e., it is numerically backward stable and preserves the structure (i.e., Hamiltonian or symplectic). In the case of a Hamiltonian matrix the method is closely related to the square reduced method of Van Loan, but in contrast to that method which may suffer from a loss of accuracy of order sqrt(epsilon), where epsilon is the machine precision, the new method computes the eigenvalues to full possible accuracy.
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A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencilsBenner, P., Mehrmann, V., Xu, H. 30 October 1998 (has links)
A new method is presented for the numerical computation of the generalized eigen- values of real Hamiltonian or symplectic pencils and matrices. The method is strongly backward stable, i.e., it is numerically backward stable and preserves the structure (i.e., Hamiltonian or symplectic). In the case of a Hamiltonian matrix the method is closely related to the square reduced method of Van Loan, but in contrast to that method which may suffer from a loss of accuracy of order sqrt(epsilon), where epsilon is the machine precision, the new method computes the eigenvalues to full possible accuracy.
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Canonical forms for Hamiltonian and symplectic matrices and pencilsMehrmann, Volker, Xu, Hongguo 09 September 2005 (has links) (PDF)
We study canonical forms for Hamiltonian and
symplectic matrices or pencils under equivalence
transformations which keep the class invariant.
In contrast to other canonical forms our forms
are as close as possible to a triangular structure
in the same class. We give necessary and
sufficient conditions for the existence of
Hamiltonian and symplectic triangular Jordan,
Kronecker and Schur forms. The presented results
generalize results of Lin and Ho [17] and simplify
the proofs presented there.
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Canonical forms for Hamiltonian and symplectic matrices and pencilsMehrmann, Volker, Xu, Hongguo 09 September 2005 (has links)
We study canonical forms for Hamiltonian and
symplectic matrices or pencils under equivalence
transformations which keep the class invariant.
In contrast to other canonical forms our forms
are as close as possible to a triangular structure
in the same class. We give necessary and
sufficient conditions for the existence of
Hamiltonian and symplectic triangular Jordan,
Kronecker and Schur forms. The presented results
generalize results of Lin and Ho [17] and simplify
the proofs presented there.
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