A numerical method for computing the Hamiltonian Schur form (Q861657)
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scientific article; zbMATH DE number 5119706
| Language | Label | Description | Also known as |
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| English | A numerical method for computing the Hamiltonian Schur form |
scientific article; zbMATH DE number 5119706 |
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A numerical method for computing the Hamiltonian Schur form (English)
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30 January 2007
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\textit{C. Paige} and \textit{C. Van Loan} [Linear Algebra Appl. 41, 11--32 (1981)] posed the open question to derive an \(O(n^3)\) method that is numerically strongly backward stable, to compute the real Hamiltonian Schur form of a Hamiltonian matrix. This problem is solved in this paper. The authors present a numerical method based on a symplectic URV-decomposition. The numerical performance of the new method indicates that if no eigenvalues of the Hamiltonian matrix are close to the imaginary axis then the method is numerically strongly backward stable.
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Hamiltonian matrix
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structured Schur form
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algorithm
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backward stability
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Riccati matrix equation
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symplectic URV-decomposition
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