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Solving Matrix Equations on Multi-Core and Many-Core Architectures

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Author(s): Peter Benner | Pablo Ezzatti | Hermann Mena | Enrique S. Quintana-Ortí | Alfredo Remón

Journal: Algorithms
ISSN 1999-4893

Volume: 6;
Issue: 4;
Start page: 857;
Date: 2013;
Original page

Keywords: control theory | Lyapunov and Riccati equations | high performance | multicore processors | GPUs

ABSTRACT
We address the numerical solution of Lyapunov, algebraic and differential Riccati equations, via the matrix sign function, on platforms equipped with general-purpose multicore processors and, optionally, one or more graphics processing units (GPUs). In particular, we review the solvers for these equations, as well as the underlying methods, analyze their concurrency and scalability and provide details on their parallel implementation. Our experimental results show that this class of hardware provides sufficient computational power to tackle large-scale problems, which only a few years ago would have required a cluster of computers.
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