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

Algorithms

Peter Benner²  Pablo Ezzatti⁴  Hermann Mena³  Enrique S. Quintana-Ortí¹ 

[1] Departamento de Ingeniería y Ciencia de Computadores, Universidad Jaime I, Av. de Vicent Sos Baynat s/n, Castellón 12071, Spain; E-Mail:;Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr 1, Magdeburg 39106, Germany; E-Mail:;Department of Mathematics, University of Innsbruck, Technikerstr. 19a, Innsbruck 6020, Austria; E-Mail:;Instituto de Computación, Univ. de la República, Julio Herrera y Reissig 565, Montevideo 11300, Uruguay; E-Mail:

关键词: control theory;    Lyapunov and Riccati equations;    high performance;    multicore processors;    GPUs;   

DOI  :  10.3390/a6040857

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.