A numerically strongly stable method for computing the Hamiltonian Schur form
| dc.contributor.author | Chu, Delin | |
| dc.contributor.author | Liu, Xinmin | |
| dc.contributor.author | Mehrmann, Volker | |
| dc.date.accessioned | 2021-12-17T10:06:00Z | |
| dc.date.available | 2021-12-17T10:06:00Z | |
| dc.date.issued | 2004-10-04 | |
| dc.description.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. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15530 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14303 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | Hamiltonian matrix | en |
| dc.subject.other | skew-Hamiltonian matrix | en |
| dc.subject.other | real Hamiltonian Schur form | en |
| dc.subject.other | real skew-Hamiltonian Schur form | en |
| dc.subject.other | symplectic URV-decomposition | en |
| dc.subject.other | stable invariant subspace | en |
| dc.title | A numerically strongly stable method for computing the Hamiltonian Schur form | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2004, 24 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 65F15 Eigenvalues, eigenvectors | en |
| tub.subject.msc2000 | 93B36 H∞-control | en |