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|Title:||A numerical method for computing the Hamiltonian Schur form|
|Authors:||Chu, D. |
|Source:||Chu, D.,Liu, X.,Mehrmann, V. (2007-01). A numerical method for computing the Hamiltonian Schur form. Numerische Mathematik 105 (3) : 375-412. ScholarBank@NUS Repository. https://doi.org/10.1007/s00211-006-0043-0|
|Abstract:||We derive a new numerical method for computing the Hamiltonian Schur form of a Hamiltonian matrix M ε ℝ2n×2n that has no purely imaginary eigenvalues. We demonstrate the properties of the new method by showing its performance for the benchmark collection of continuous-time algebraic Riccati equations. Despite the fact that no complete error analysis for the method is yet available, the numerical results indicate that if no eigenvalues of M are close to the imaginary axis then the method computes the exact Hamiltonian Schur form of a nearby Hamiltonian matrix and thus is numerically strongly backward stable. The new method is of complexity O(n 3) and hence it solves a long-standing open problem in numerical analysis. © 2006 Springer-Verlag.|
|Source Title:||Numerische Mathematik|
|Appears in Collections:||Staff Publications|
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