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Algorithms 2013, 6(4), 857-870; doi:10.3390/a6040857

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

1 Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr 1, Magdeburg 39106, Germany 2 Instituto de Computación, Univ. de la República, Julio Herrera y Reissig 565, Montevideo 11300, Uruguay 3 Department of Mathematics, University of Innsbruck, Technikerstr. 19a, Innsbruck 6020, Austria 4 Departamento de Ingeniería y Ciencia de Computadores, Universidad Jaime I, Av. de Vicent Sos Baynat s/n, Castellón 12071, Spain
* Author to whom correspondence should be addressed.
Received: 27 September 2013 / Revised: 12 November 2013 / Accepted: 18 November 2013 / Published: 25 November 2013
(This article belongs to the Special Issue Algorithms for Multi Core Parallel Computation)
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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.
Keywords: control theory; Lyapunov and Riccati equations; high performance; multicore processors; GPUs control theory; Lyapunov and Riccati equations; high performance; multicore processors; GPUs
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Benner, P.; Ezzatti, P.; Mena, H.; Quintana-Ortí, E.S.; Remón, A. Solving Matrix Equations on Multi-Core and Many-Core Architectures. Algorithms 2013, 6, 857-870.

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