Solving matrix equations on multi-core and many-core architectures. (English) Zbl 1461.65061

Summary: 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.


65F45 Numerical methods for matrix equations
15A24 Matrix equations and identities
65Y10 Numerical algorithms for specific classes of architectures


Full Text: DOI


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