dc.contributor.author Benner, Peter dc.contributor.author Byers, Ralph dc.contributor.author Mehrmann, Volker dc.contributor.author Xu, Hongguo dc.date.accessioned 2005-05-02T15:01:55Z dc.date.available 2005-05-02T15:01:55Z dc.date.issued 2002-07-09 dc.identifier.citation Benner, P; Byers, R; Mehrmann, V; Xu, HG. Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. July 9 2002. 24(1):165-190. dc.identifier.other ISI:000177412600014 dc.identifier.uri http://hdl.handle.net/1808/373 dc.description Working title was “Numerical Computation of Deflating Subspaces of Embedded Hamiltonian and Symplectic Pencils" dc.description.abstract We discuss the numerical solution of structured generalized eigenvalue problems that arise from linear- quadratic optimal control problems, H infinity optimization, multibody systems, and many other areas of applied mathematics, physics, and chemistry. The classical approach for these problems requires computing invariant and deflating subspaces of matrices and matrix pencils with Hamiltonian and/ or skew- Hamiltonian structure. We extend the recently developed methods for Hamiltonian matrices to the general case of skew- Hamiltonian/ Hamiltonian pencils. The algorithms circumvent problems with skew- Hamiltonian/ Hamiltonian matrix pencils that lack structured Schur forms by embedding them into matrix pencils that always admit a structured Schur form. The rounding error analysis of the resulting algorithms is favorable. For the embedded matrix pencils, the algorithms use structure- preserving unitary matrix computations and are strongly backwards stable, i. e., they compute the exact structured Schur form of a nearby matrix pencil with the same structure. dc.description.sponsorship All authors were partially supported by Deutsche Forschungsgemeinschaft, Research Grant Me 790/7-2 and Sonderforschungsbereich 393, “Numerische Simulation auf massiv parallelen Rechnern”. dc.format.extent 284757 bytes dc.format.mimetype application/pdf dc.language.iso en_US dc.publisher SIAM PUBLICATIONS dc.subject Eigenvalue problem dc.subject Deflating subspace dc.subject Hamiltonian matrix dc.subject Skew-hamiltonian matrix dc.subject Skew-hamiltonian/hamiltonian matrix pencil dc.title Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils dc.type Article dc.identifier.doi 10.1137/S0895479800367439 dc.rights.accessrights openAccess
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