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