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Main Title: A numerically strongly stable method for computing the Hamiltonian Schur form
Author(s): Chu, Delin
Liu, Xinmin
Mehrmann, Volker
Type: Research Paper
Abstract: In this paper we solve a long-standing open problem in numerical analysis called 'Van Loan's Curse'. We derive a new numerical method for computing the Hamiltonian Schur form of a Hamiltonian matrix that has no purely imaginary eigenvalues. The proposed method is numerically strongly backward stable, i.e., it computes the exact Hamiltonian Schur form of a nearby Hamiltonian matrix, and it is of complexity O(n^3) and thus Van Loan's curse is lifted. We demonstrate the quality of the new method by showing its performance for the benchmark collection of continuous-time algebraic Riccati equations.
Subject(s): Hamiltonian matrix
skew-Hamiltonian matrix
real Hamiltonian Schur form
real skew-Hamiltonian Schur form
symplectic URV-decomposition
stable invariant subspace
Issue Date: 4-Oct-2004
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65F15 Eigenvalues, eigenvectors
93B36 H∞-control
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2004, 24
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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