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

Shank, Stephen David
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Genre
Thesis/Dissertation
Date
2014
Advisor
Szyld, Daniel
Simoncini, V. (Valeria)
Committee member
Seibold, Benjamin
Yang, Wei-shih, 1954-
Group
Department
Mathematics
Subject
Applied Mathematics
 Krylov Subspaces
 Low Rank
 Matrix Equations
 Numerical Linear Algebra
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http://hdl.handle.net/20.500.12613/3556
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TETDEDXShank-temple-0225E-11829.pdf
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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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