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    Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils

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    Issue Date
    2002-07-09
    Author
    Benner, Peter
    Byers, Ralph
    Mehrmann, Volker
    Xu, Hongguo
    Publisher
    SIAM PUBLICATIONS
    Format
    284757 bytes
    Type
    Article
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    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.
    Description
    Working title was “Numerical Computation of Deflating Subspaces of Embedded Hamiltonian and Symplectic Pencils"
    URI
    http://hdl.handle.net/1808/373
    DOI
    https://doi.org/10.1137/S0895479800367439
    Collections
    • Mathematics Scholarly Works [282]
    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.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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