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    Low-rank solution methods for large-scale linear matrix equations

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    Genre
    Thesis/Dissertation
    Date
    2014
    Author
    Shank, Stephen David
    Advisor
    Szyld, Daniel
    Simoncini, V. (Valeria)
    Committee member
    Seibold, Benjamin
    Yang, Wei-shih, 1954-
    Department
    Mathematics
    Subject
    Applied Mathematics
    Krylov Subspaces
    Low Rank
    Matrix Equations
    Numerical Linear Algebra
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/3556
    
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    DOI
    http://dx.doi.org/10.34944/dspace/3538
    Abstract
    We consider low-rank solution methods for certain classes of large-scale linear matrix equations. Our aim is to adapt existing low-rank solution methods based on standard, extended and rational Krylov subspaces to solve equations which may viewed as extensions of the classical Lyapunov and Sylvester equations. The first class of matrix equations that we consider are constrained Sylvester equations, which essentially consist of Sylvester's equation along with a constraint on the solution matrix. These therefore constitute a system of matrix equations. The second are generalized Lyapunov equations, which are Lyapunov equations with additional terms. Such equations arise as computational bottlenecks in model order reduction.
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