A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils | Zendy

Peter Benner | Zendy; Volker Mehrmann | Zendy; Hongguo Xu | Zendy

Open Access

A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils

Author(s) -

Peter Benner,

Volker Mehrmann,

Hongguo Xu

Publication year - 1998

Publication title -

numerische mathematik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.214

H-Index - 90

eISSN - 0945-3245

pISSN - 0029-599X

DOI - 10.1007/s002110050315

Subject(s) - symplectic geometry , mathematics , eigenvalues and eigenvectors , computation , hamiltonian matrix , numerical analysis , hamiltonian (control theory) , symplectic matrix , hamiltonian system , mathematical analysis , pure mathematics , symplectic manifold , algorithm , symplectic representation , symmetric matrix , mathematical optimization , quantum mechanics , physics

. A new method is presented for the numerical computation of the generalized eigenvalues of real Hamiltonian or symplectic pencils and matrices. The method 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 , where is the machine precision, the new method computes the eigenvalues to full possible accuracy.

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